Method and apparatus to determine a patterning process parameter

ABSTRACT

A method of configuring a parameter determination process, the method including: obtaining a mathematical model of a structure, the mathematical model configured to predict an optical response when illuminating the structure with a radiation beam and the structure having geometric symmetry at a nominal physical configuration; using, by a hardware computer system, the mathematical model to simulate a perturbation in the physical configuration of the structure of a certain amount to determine a corresponding change of the optical response in each of a plurality of pixels to obtain a plurality of pixel sensitivities; and based on the pixel sensitivities, determining a plurality of weights for combination with measured pixel optical characteristic values of the structure on a substrate to yield a value of a parameter associated with change in the physical configuration, each weight corresponding to a pixel.

This application is a divisional of U.S. patent application Ser. No.15/445,536, filed Feb. 28, 2017, now allowed, which claims the benefitof priority under 35 USC § 119(e) to U.S. Provisional Patent ApplicationNo. 62/301,880, filed Mar. 1, 2016, to U.S. Provisional PatentApplication No. 62/435,662, filed Dec. 16, 2016, to U.S. ProvisionalPatent Application No. 62/435,670, filed Dec. 16, 2016, to U.S.Provisional Patent Application No. 62/435,649, filed Dec. 16, 2016, toU.S. Provisional Patent Application No. 62/435,630, filed Dec. 16, 2016and to U.S. Provisional Patent Application No. 62/458,932, filed Feb.14, 2017, each of the foregoing applications incorporated herein itsentirety by reference.

FIELD

The present description relates to a method and apparatus to determine aparameter (such as overlay) of a process, for example, to create apattern on a substrate and which determined parameter can be used todesign, monitor, adjust, etc. one or more variables related to theprocessing.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs) or other devices designed to be functional. Inthat instance, a patterning device, which is alternatively referred toas a mask or a reticle, may be used to generate a circuit pattern to beformed on an individual layer of the device designed to be functional.This pattern can be transferred onto a target portion (e.g., includingpart of, one, or several dies) on a substrate (e.g., a silicon wafer).Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. Known lithographic apparatusinclude so-called steppers, in which each target portion is irradiatedby exposing an entire pattern onto the target portion at one time, andso-called scanners, in which each target portion is irradiated byscanning the pattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrateparallel or anti parallel to this direction. It is also possible totransfer the pattern from the patterning device to the substrate byimprinting the pattern onto the substrate.

SUMMARY

Manufacturing devices, such as semiconductor devices, typically involvesprocessing a substrate (e.g., a semiconductor wafer) using a number offabrication processes to form various features and often multiple layersof the devices. Such layers and/or features are typically manufacturedand processed using, e.g., deposition, lithography, etch,chemical-mechanical polishing, and ion implantation. Multiple devicesmay be fabricated on a plurality of dies on a substrate and thenseparated into individual devices. This device manufacturing process maybe considered a patterning process. A patterning process involves apattern transfer step, such as optical and/or nanoimprint lithographyusing a lithographic apparatus, to provide a pattern on a substrate andtypically, but optionally, involves one or more related patternprocessing steps, such as resist development by a development apparatus,baking of the substrate using a bake tool, etching the pattern by anetch apparatus, etc. Further, one or more metrology processes areinvolved in the patterning process.

Metrology processes are used at various steps during a patterningprocess to monitor and/or control the process. For example, metrologyprocesses are used to measure one or more characteristics of asubstrate, such as a relative location (e.g., registration, overlay,alignment, etc.) or dimension (e.g., line width, critical dimension(CD), thickness, etc.) of features formed on the substrate during thepatterning process, such that, for example, the performance of thepatterning process can be determined from the one or morecharacteristics. If the one or more characteristics are unacceptable(e.g., out of a predetermined range for the characteristic(s)), one ormore variables of the patterning process may be designed or altered,e.g., based on the measurements of the one or more characteristics, suchthat substrates manufactured by the patterning process have anacceptable characteristic(s).

With the advancement of lithography and other patterning processtechnologies, the dimensions of functional elements have continuallybeen reduced while the amount of the functional elements, such astransistors, per device has been steadily increased over decades. In themeanwhile, the requirement of accuracy in terms of overlay, criticaldimension (CD), etc. has become more and more stringent. Error, such aserror in overlay, error in CD, etc., will inevitably be produced in thepatterning process. For example, imaging error may be produced fromoptical aberration, patterning device heating, patterning device error,and/or substrate heating and can be characterized in terms of, e.g.,overlay, CD, etc. Additionally or alternatively, error may be introducedin other parts of the patterning process, such as in etch, development,bake, etc. and similarly can be characterized in terms of, e.g.,overlay, CD, etc. The error may cause a problem in terms of thefunctioning of the device, including failure of the device to functionor one or more electrical problems of the functioning device.Accordingly, it is desirable to be able to characterize one or morethese errors and take steps to design, modify, control, etc. apatterning process to reduce or minimize one or more of these errors.

In an embodiment, there is provided a method of configuring a parameterdetermination process, the method comprising: obtaining a mathematicalmodel of a structure, the mathematical model configured to predict anoptical response when illuminating the structure with a radiation beamand the structure having geometric symmetry at a nominal physicalconfiguration; using, by a hardware computer system, the mathematicalmodel to simulate a perturbation in the physical configuration of thestructure of a certain amount to determine a corresponding change of theoptical response in each of a plurality of pixels to obtain a pluralityof pixel sensitivities; and based on the pixel sensitivities,determining a plurality of weights for combination with measured pixeloptical characteristic values of the structure on a substrate to yield avalue of a parameter associated with change in the physicalconfiguration, each weight corresponding to a pixel.

In an embodiment, there is provided a method comprising: using, by ahardware computer system, a mathematical model of a structure to predictan optical response when illuminating the structure with a radiationbeam, the structure having geometric symmetry at a nominal physicalconfiguration and a patterning process parameter measures change in thephysical configuration; and using, by the hardware computer system, anon-linear solver to determine, based on the optical response,coefficients of a mathematical function of the patterning processparameter as a variable thereof, the determined coefficients and thefunction for use with a measured representation of detected radiationfrom the structure, on a substrate, at a different physicalconfiguration than the nominal physical configuration which causes anasymmetric optical characteristic distribution in the detectedrepresentation, to determine a value of the patterning process parameterfor the measured structure.

In an embodiment, there is provided a method, comprising: obtainingmeasurement results for different instances of a structure generated bya patterning process, wherein measurement results are obtained at eachof a plurality of different set values of a patterning process parameterthat measures a change in the physical configuration of the structureand each different set value of the patterning process parametercorresponds to a physical configuration of the structure that causes anasymmetric optical characteristic distribution in a radiationrepresentation; and determining, by a hardware computer system, aplurality of data-driven values that correspond to weights forcombination with measured optical characteristic values of a furtherinstance of the structure to yield a value of the patterning processparameter, wherein the set values and the measurement results are usedin an objective or merit function or a machine learning algorithm, todetermine the data-driven values.

In an aspect, there is provided a non-transitory computer programproduct comprising machine-readable instructions for causing a processorsystem to cause performance of a method described herein. In an aspect,there is provided a computer program product comprising a computernon-transitory readable medium having instructions recorded thereon, theinstructions when executed by a computer implementing a method or one ormore process steps described herein.

In an aspect, there is provided a metrology apparatus for measuring anobject of a patterning process, the metrology apparatus configured toperform a method as described herein. In an aspect, there is provided aninspection apparatus for inspecting an object of a patterning process,the inspection apparatus being operable to perform a method as describedherein.

In an aspect, there is provided a system comprising: a metrologyapparatus configured to provide a beam of radiation onto an objectsurface and to detect radiation redirected by the structure on theobject surface; and a computer program product as described herein. Inan embodiment, the system further comprises a lithographic apparatuscomprising a support structure configured to hold a patterning device tomodulate a radiation beam and a projection optical system arranged toproject the modulated radiation beam onto a radiation-sensitivesubstrate, wherein the object is the substrate.

In an embodiment, there is provided a system comprising: a hardwareprocessor system; and a non-transitory computer readable storage mediumconfigured to store machine-readable instructions, wherein whenexecuted, the machine-readable instructions cause the hardware processorsystem to perform a method as described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying drawings in which:

FIG. 1 schematically depicts an embodiment of a lithographic apparatus;

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster;

FIG. 3A is schematic diagram of a measurement apparatus for use inmeasuring targets according to an embodiment using a first pair ofillumination apertures providing certain illumination modes;

FIG. 3B is a schematic detail of a diffraction spectrum of a target fora given direction of illumination;

FIG. 3C is a schematic illustration of a second pair of illuminationapertures providing further illumination modes in using a measurementapparatus for diffraction based overlay measurements;

FIG. 3D is a schematic illustration of a third pair of illuminationapertures combining the first and second pairs of apertures providingfurther illumination modes in using a measurement apparatus fordiffraction based overlay measurements;

FIG. 4 schematically depicts a form of multiple periodic structure(e.g., multiple grating) target and an outline of a measurement spot ona substrate;

FIG. 5 schematically depicts an image of the target of FIG. 4 obtainedin the apparatus of FIG. 3;

FIG. 6 schematically depicts an example metrology apparatus andmetrology technique;

FIG. 7 schematically depicts an example metrology apparatus;

FIG. 8 illustrates the relationship between an illumination spot of ametrology apparatus and a metrology target;

FIG. 9 schematically depicts a process of deriving one or more variablesof interest based on measurement data;

FIG. 10A schematically depicts an example unit cell, an associated pupilrepresentation, and an associated derived pupil representation;

FIG. 10B schematically depicts an example unit cell, an associated pupilrepresentation, and an associated derived pupil representation;

FIG. 10C schematically depicts an example target comprising one or morephysical instances of a unit cell;

FIG. 11 depicts a high-level flow of obtaining weightings fordetermining a patterning process parameter from measured radiation;

FIG. 12 depicts a high-level flow of determining a patterning processparameter from measured radiation;

FIG. 13 depicts a high-level flow of an embodiment of a data driventechnique;

FIG. 14 depicts a high-level flow of an embodiment of a data driventechnique in combination with a physical geometric model;

FIG. 15 depicts a high-level flow of an embodiment of a data driventechnique in combination with a physical geometric model;

FIG. 16 depicts a high-level flow of an embodiment of a data driventechnique in combination with a physical geometric model;

FIG. 17 depicts a high-level flow of an embodiment of a data driventechnique in combination with a physical geometric model;

FIG. 18 schematically depicts an embodiment of a multiple overlay unitcell of a target;

FIG. 19 schematically depicts an embodiment of a multiple overlay unitcell of a target;

FIG. 20 depicts an example graph of two vectors corresponding to twodifferent overlays;

FIG. 21A and FIG. 21B schematically depict an example of a non-producttarget design;

FIG. 22A, FIG. 22B, FIG. 22C and FIG. 22D schematically depict examplesof a non-product target design;

FIG. 23A and FIG. 23B schematically depict an example of a non-producttarget design;

FIG. 24A and FIG. 24B schematically depict an example of a non-producttarget design;

FIG. 25A and FIG. 25B schematically depict an example of a non-producttarget design;

FIG. 26A, FIG. 26B and FIG. 26C schematically depict an example of anon-product target design;

FIG. 27A and FIG. 27B schematically depict an example of a non-producttarget design;

FIG. 28A, FIG. 28B and FIG. 28C schematically depict an example of anon-product target design;

FIG. 29A schematically depicts an example of device pattern features;

FIG. 29B, FIG. 29C, FIG. 29D and FIG. 29E schematically depict anexample of steps of a device patterning process;

FIG. 29F schematically depicts an example of structures of a non-producttarget design corresponding to the steps of FIGS. 29B and 29D;

FIG. 29G schematically depicts an example of a non-product target designcreated from the structures of FIG. 29F;

FIG. 30A schematically depicts an example of device pattern features;

FIG. 30B schematically depicts an example of structures of a non-producttarget design;

FIG. 30C schematically depicts an example of a non-product target designcreated from the structures of FIG. 30B;

FIG. 31 corresponds to an embodiment of a method of designing anon-product target design; and

FIG. 32 schematically depicts a computer system which may implementembodiments of this disclosure.

DETAILED DESCRIPTION

Before describing embodiments in detail, it is instructive to present anexample environment in which embodiments may be implemented.

FIG. 1 schematically depicts a lithographic apparatus LA. The apparatuscomprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. UV radiation or DUV radiation);    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist-coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate in accordance with certain parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies) of the substrate W, the projection        system supported on a reference frame (RF).

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The support structure supports the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a pattern in atarget portion of the substrate. In an embodiment, a patterning deviceis any device that can be used to impart a radiation beam with a patternin its cross-section so as to create a pattern in a target portion ofthe substrate. It should be noted that the pattern imparted to theradiation beam may not exactly correspond to the desired pattern in thetarget portion of the substrate, for example if the pattern includesphase-shifting features or so called assist features. Generally, thepattern imparted to the radiation beam will correspond to a particularfunctional layer in a device being created in the target portion, suchas an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

The projection system PS has an optical transfer function which may benon-uniform, which can affect the pattern imaged on the substrate W. Forunpolarized radiation such effects can be fairly well described by twoscalar maps, which describe the transmission (apodization) and relativephase (aberration) of radiation exiting the projection system PS as afunction of position in a pupil plane thereof. These scalar maps, whichmay be referred to as the transmission map and the relative phase map,may be expressed as a linear combination of a complete set of basisfunctions. A particularly convenient set is the Zernike polynomials,which form a set of orthogonal polynomials defined on a unit circle. Adetermination of each scalar map may involve determining thecoefficients in such an expansion. Since the Zernike polynomials areorthogonal on the unit circle, the Zernike coefficients may bedetermined by calculating the inner product of a measured scalar mapwith each Zernike polynomial in turn and dividing this by the square ofthe norm of that Zernike polynomial.

The transmission map and the relative phase map are field and systemdependent. That is, in general, each projection system PS will have adifferent Zernike expansion for each field point (i.e. for each spatiallocation in its image plane). The relative phase of the projectionsystem PS in its pupil plane may be determined by projecting radiation,for example from a point-like source in an object plane of theprojection system PS (i.e. the plane of the patterning device MA),through the projection system PS and using a shearing interferometer tomeasure a wavefront (i.e. a locus of points with the same phase). Ashearing interferometer is a common path interferometer and therefore,advantageously, no secondary reference beam is required to measure thewavefront. The shearing interferometer may comprise a diffractiongrating, for example a two dimensional grid, in an image plane of theprojection system (i.e. the substrate table WT) and a detector arrangedto detect an interference pattern in a plane that is conjugate to apupil plane of the projection system PS. The interference pattern isrelated to the derivative of the phase of the radiation with respect toa coordinate in the pupil plane in the shearing direction. The detectormay comprise an array of sensing elements such as, for example, chargecoupled devices (CCDs).

The projection system PS of a lithography apparatus may not producevisible fringes and therefore the accuracy of the determination of thewavefront can be enhanced using phase stepping techniques such as, forexample, moving the diffraction grating. Stepping may be performed inthe plane of the diffraction grating and in a direction perpendicular tothe scanning direction of the measurement. The stepping range may be onegrating period, and at least three (uniformly distributed) phase stepsmay be used. Thus, for example, three scanning measurements may beperformed in the y-direction, each scanning measurement being performedfor a different position in the x-direction. This stepping of thediffraction grating effectively transforms phase variations intointensity variations, allowing phase information to be determined. Thegrating may be stepped in a direction perpendicular to the diffractiongrating (z direction) to calibrate the detector.

The transmission (apodization) of the projection system PS in its pupilplane may be determined by projecting radiation, for example from apoint-like source in an object plane of the projection system PS (i.e.the plane of the patterning device MA), through the projection system PSand measuring the intensity of radiation in a plane that is conjugate toa pupil plane of the projection system PS, using a detector. The samedetector as is used to measure the wavefront to determine aberrationsmay be used.

The projection system PS may comprise a plurality of optical (e.g.,lens) elements and may further comprise an adjustment mechanism AMconfigured to adjust one or more of the optical elements so as tocorrect for aberrations (phase variations across the pupil planethroughout the field). To achieve this, the adjustment mechanism may beoperable to manipulate one or more optical (e.g., lens) elements withinthe projection system PS in one or more different ways. The projectionsystem may have a co-ordinate system wherein its optical axis extends inthe z direction. The adjustment mechanism may be operable to do anycombination of the following: displace one or more optical elements;tilt one or more optical elements; and/or deform one or more opticalelements. Displacement of an optical element may be in any direction (x,y, z or a combination thereof). Tilting of an optical element istypically out of a plane perpendicular to the optical axis, by rotatingabout an axis in the x and/or y directions although a rotation about thez axis may be used for a non-rotationally symmetric aspherical opticalelement. Deformation of an optical element may include a low frequencyshape (e.g. astigmatic) and/or a high frequency shape (e.g. free formaspheres). Deformation of an optical element may be performed forexample by using one or more actuators to exert force on one or moresides of the optical element and/or by using one or more heatingelements to heat one or more selected regions of the optical element. Ingeneral, it may not be possible to adjust the projection system PS tocorrect for apodization (transmission variation across the pupil plane).The transmission map of a projection system PS may be used whendesigning a patterning device (e.g., mask) MA for the lithographyapparatus LA. Using a computational lithography technique, thepatterning device MA may be designed to at least partially correct forapodization.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore tables (e.g., two or more substrate tables WTa, WTb, two or morepatterning device tables, a substrate table WTa and a table WTb belowthe projection system without a substrate that is dedicated to, forexample, facilitating measurement, and/or cleaning, etc.). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure. For example, alignmentmeasurements using an alignment sensor AS and/or level (height, tilt,etc.) measurements using a level sensor LS may be made.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the patterning device and the projection system. Immersiontechniques are well known in the art for increasing the numericalaperture of projection systems. The term “immersion” as used herein doesnot mean that a structure, such as a substrate, must be submerged inliquid, but rather only means that liquid is located between theprojection system and the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD configured to adjust theangular intensity distribution of the radiation beam. Generally, atleast the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in apupil plane of the illuminator can be adjusted. In addition, theilluminator IL may comprise various other components, such as anintegrator IN and a condenser CO. The illuminator may be used tocondition the radiation beam, to have a desired uniformity and intensitydistribution in its cross-section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., mask table) MT, and ispatterned by the patterning device. Having traversed the patterningdevice MA, the radiation beam B passes through the projection system PS,which focuses the beam onto a target portion C of the substrate W. Withthe aid of the second positioner PW and position sensor IF (e.g. aninterferometric device, linear encoder, 2-D encoder or capacitivesensor), the substrate table WT can be moved accurately, e.g. so as toposition different target portions C in the path of the radiation beamB. Similarly, the first positioner PM and another position sensor (whichis not explicitly depicted in FIG. 1) can be used to accurately positionthe patterning device MA with respect to the path of the radiation beamB, e.g. after mechanical retrieval from a mask library, or during ascan. In general, movement of the support structure MT may be realizedwith the aid of a long-stroke module (coarse positioning) and ashort-stroke module (fine positioning), which form part of the firstpositioner PM. Similarly, movement of the substrate table WT may berealized using a long-stroke module and a short-stroke module, whichform part of the second positioner PW. In the case of a stepper (asopposed to a scanner) the support structure MT may be connected to ashort-stroke actuator only, or may be fixed. Patterning device MA andsubstrate W may be aligned using patterning device alignment marks M1,M2 and substrate alignment marks P1, P2. Although the substratealignment marks as illustrated occupy dedicated target portions, theymay be located in spaces between target portions (these are known asscribe-lane alignment marks). Similarly, in situations in which morethan one die is provided on the patterning device MA, the patterningdevice alignment marks may be located between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the support structure MT and the substrate table WT arekept essentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the support structure MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the supportstructure MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PS. In scan mode, themaximum size of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the support structure MT is kept essentiallystationary holding a programmable patterning device, and the substratetable WT is moved or scanned while a pattern imparted to the radiationbeam is projected onto a target portion C. In this mode, generally apulsed radiation source is employed and the programmable patterningdevice is updated as required after each movement of the substrate tableWT or in between successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

As shown in FIG. 2, the lithographic apparatus LA may form part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatuses to perform pre- and post-exposureprocesses on a substrate. Conventionally these include one or more spincoaters SC to deposit one or more resist layers, one or more developersDE to develop exposed resist, one or more chill plates CH and/or one ormore bake plates BK. A substrate handler, or robot, RO picks up one ormore substrates from input/output port I/O1, I/O2, moves them betweenthe different process apparatuses and delivers them to the loading bayLB of the lithographic apparatus. These apparatuses, which are oftencollectively referred to as the track, are under the control of a trackcontrol unit TCU which is itself controlled by the supervisory controlsystem SCS, which also controls the lithographic apparatus vialithography control unit LACU. Thus, the different apparatuses can beoperated to maximize throughput and processing efficiency.

In order that a substrate that is exposed by the lithographic apparatusis exposed correctly and consistently, it is desirable to inspect anexposed substrate to measure or determine one or more properties such asoverlay (which can be, for example, between structures in overlyinglayers or between structures in a same layer that have been providedseparately to the layer by, for example, a double patterning process),line thickness, critical dimension (CD), focus offset, a materialproperty, etc. Accordingly a manufacturing facility in which lithocellLC is located also typically includes a metrology system MET whichreceives some or all of the substrates W that have been processed in thelithocell. The metrology system MET may be part of the lithocell LC, forexample it may be part of the lithographic apparatus LA.

Metrology results may be provided directly or indirectly to thesupervisory control system SCS. If an error is detected, an adjustmentmay be made to exposure of a subsequent substrate (especially if theinspection can be done soon and fast enough that one or more othersubstrates of the batch are still to be exposed) and/or to subsequentexposure of the exposed substrate. Also, an already exposed substratemay be stripped and reworked to improve yield, or discarded, therebyavoiding performing further processing on a substrate known to befaulty. In a case where only some target portions of a substrate arefaulty, further exposures may be performed only on those target portionswhich are good.

Within a metrology system MET, a metrology apparatus is used todetermine one or more properties of the substrate, and in particular,how one or more properties of different substrates vary or differentlayers of the same substrate vary from layer to layer. The metrologyapparatus may be integrated into the lithographic apparatus LA or thelithocell LC or may be a stand-alone device. To enable rapidmeasurement, it is desirable that the metrology apparatus measure one ormore properties in the exposed resist layer immediately after theexposure. However, the latent image in the resist has a lowcontrast—there is only a very small difference in refractive indexbetween the parts of the resist which have been exposed to radiation andthose which have not—and not all metrology apparatus have sufficientsensitivity to make useful measurements of the latent image. Thereforemeasurements may be taken after the post-exposure bake step (PEB) whichis customarily the first step carried out on an exposed substrate andincreases the contrast between exposed and unexposed parts of theresist. At this stage, the image in the resist may be referred to assemi-latent. It is also possible to make measurements of the developedresist image—at which point either the exposed or unexposed parts of theresist have been removed—or after a pattern transfer step such asetching. The latter possibility limits the possibilities for rework of afaulty substrate but may still provide useful information.

To enable the metrology, one or more targets can be provided on thesubstrate. In an embodiment, the target is specially designed and maycomprise a periodic structure. In an embodiment, the target is a part ofa device pattern, e.g., a periodic structure of the device pattern. Inan embodiment, the device pattern is a periodic structure of a memorydevice (e.g., a Bipolar Transistor (BPT), a Bit Line Contact (BLC), etc.structure).

In an embodiment, the target on a substrate may comprise one or more 1-Dperiodic structures (e.g., gratings), which are printed such that afterdevelopment, the periodic structural features are formed of solid resistlines. In an embodiment, the target may comprise one or more 2-Dperiodic structures (e.g., gratings), which are printed such that afterdevelopment, the one or more periodic structures are formed of solidresist pillars or vias in the resist. The bars, pillars or vias mayalternatively be etched into the substrate (e.g., into one or morelayers on the substrate).

In an embodiment, one of the parameters of interest of a patterningprocess is overlay. Overlay can be measured using dark fieldscatterometry in which the zeroth order of diffraction (corresponding toa specular reflection) is blocked, and only higher orders processed.Examples of dark field metrology can be found in PCT patent applicationpublication nos. WO 2009/078708 and WO 2009/106279, which are herebyincorporated in their entirety by reference. Further developments of thetechnique have been described in U.S. patent application publicationsUS2011-0027704, US2011-0043791 and US2012-0242970, which are herebyincorporated in their entirety by reference. Diffraction-based overlayusing dark-field detection of the diffraction orders enables overlaymeasurements on smaller targets. These targets can be smaller than theillumination spot and may be surrounded by device product structures ona substrate. In an embodiment, multiple targets can be measured in oneradiation capture.

A metrology apparatus suitable for use in embodiments to measure, e.g.,overlay is schematically shown in FIG. 3A. A target T (comprising aperiodic structure such as a grating) and diffracted rays areillustrated in more detail in FIG. 3B. The metrology apparatus may be astand-alone device or incorporated in either the lithographic apparatusLA, e.g., at the measurement station, or the lithographic cell LC. Anoptical axis, which has several branches throughout the apparatus, isrepresented by a dotted line O. In this apparatus, radiation emitted byan output 11 (e.g., a source such as a laser or a xenon lamp or anopening connected to a source) is directed onto substrate W via a prism15 by an optical system comprising lenses 12, 14 and objective lens 16.These lenses are arranged in a double sequence of a 4F arrangement. Adifferent lens arrangement can be used, provided that it still providesa substrate image onto a detector.

In an embodiment, the lens arrangement allows for access of anintermediate pupil-plane for spatial-frequency filtering. Therefore, theangular range at which the radiation is incident on the substrate can beselected by defining a spatial intensity distribution in a plane thatpresents the spatial spectrum of the substrate plane, here referred toas a (conjugate) pupil plane. In particular, this can be done, forexample, by inserting an aperture plate 13 of suitable form betweenlenses 12 and 14, in a plane which is a back-projected image of theobjective lens pupil plane. In the example illustrated, aperture plate13 has different forms, labeled 13N and 13S, allowing differentillumination modes to be selected. The illumination system in thepresent examples forms an off-axis illumination mode. In the firstillumination mode, aperture plate 13N provides off-axis illuminationfrom a direction designated, for the sake of description only, as‘north’. In a second illumination mode, aperture plate 13S is used toprovide similar illumination, but from an opposite direction, labeled‘south’. Other modes of illumination are possible by using differentapertures. The rest of the pupil plane is desirably dark as anyunnecessary radiation outside the desired illumination mode mayinterfere with the desired measurement signals.

As shown in FIG. 3B, target T is placed with substrate W substantiallynormal to the optical axis O of objective lens 16. A ray of illuminationI impinging on target T from an angle off the axis O gives rise to azeroth order ray (solid line 0) and two first order rays (dot-chain line+1 and double dot-chain line −1). With an overfilled small target T,these rays are just one of many parallel rays covering the area of thesubstrate including metrology target T and other features. Since theaperture in plate 13 has a finite width (necessary to admit a usefulquantity of radiation), the incident rays I will in fact occupy a rangeof angles, and the diffracted rays 0 and +1/−1 will be spread outsomewhat. According to the point spread function of a small target, eachorder +1 and −1 will be further spread over a range of angles, not asingle ideal ray as shown. Note that the periodic structure pitch andillumination angle can be designed or adjusted so that the first orderrays entering the objective lens are closely aligned with the centraloptical axis. The rays illustrated in FIGS. 3A and 3B are shown somewhatoff axis, purely to enable them to be more easily distinguished in thediagram. At least the 0 and +1 orders diffracted by the target onsubstrate W are collected by objective lens 16 and directed back throughprism 15.

Returning to FIG. 3A, both the first and second illumination modes areillustrated, by designating diametrically opposite apertures labeled asnorth (N) and south (S). When the incident ray I is from the north sideof the optical axis, that is when the first illumination mode is appliedusing aperture plate 13N, the +1 diffracted rays, which are labeled+1(N), enter the objective lens 16. In contrast, when the secondillumination mode is applied using aperture plate 13S the −1 diffractedrays (labeled −1(S)) are the ones which enter the lens 16. Thus, in anembodiment, measurement results are obtained by measuring the targettwice under certain conditions, e.g., after rotating the target orchanging the illumination mode or changing the imaging mode to obtainseparately the −1st and the +1st diffraction order intensities.Comparing these intensities for a given target provides a measurement ofasymmetry in the target, and asymmetry in the target can be used as anindicator of a parameter of a lithography process, e.g., overlay. In thesituation described above, the illumination mode is changed.

A beam splitter 17 divides the diffracted beams into two measurementbranches. In a first measurement branch, optical system 18 forms adiffraction spectrum (pupil plane image) of the target on first sensor19 (e.g. a CCD or CMOS sensor) using the zeroth and first orderdiffractive beams. Each diffraction order hits a different point on thesensor, so that image processing can compare and contrast orders. Thepupil plane image captured by sensor 19 can be used for focusing themetrology apparatus and/or normalizing intensity measurements. The pupilplane image can also be used for other measurement purposes such asreconstruction, as described further hereafter.

In the second measurement branch, optical system 20, 22 forms an imageof the target on the substrate Won sensor 23 (e.g. a CCD or CMOSsensor). In the second measurement branch, an aperture stop 21 isprovided in a plane that is conjugate to the pupil-plane of theobjective lens 16. Aperture stop 21 functions to block the zeroth orderdiffracted beam so that the image of the target formed on sensor 23 isformed from the −1 or +1 first order beam. Data regarding the imagesmeasured by sensors 19 and 23 are output to processor and controller PU,the function of which will depend on the particular type of measurementsbeing performed. Note that the term ‘image’ is used in a broad sense. Animage of the periodic structure features (e.g., grating lines) as suchwill not be formed, if only one of the −1 and +1 orders is present.

The particular forms of aperture plate 13 and stop 21 shown in FIG. 3are purely examples. In another embodiment, on-axis illumination of thetargets is used and an aperture stop with an off-axis aperture is usedto pass substantially only one first order of diffracted radiation tothe sensor. In yet other embodiments, 2nd, 3rd and higher order beams(not shown in FIG. 3) can be used in measurements, instead of or inaddition to the first order beams.

In order to make the illumination adaptable to these different types ofmeasurement, the aperture plate 13 may comprise a number of aperturepatterns formed around a disc, which rotates to bring a desired patterninto place. Note that aperture plate 13N or 13S are used to measure aperiodic structure of a target oriented in one direction (X or Ydepending on the set-up). For measurement of an orthogonal periodicstructure, rotation of the target through 90° and 270° might beimplemented. Different aperture plates are shown in FIGS. 3C and D. FIG.3C illustrates two further types of off-axis illumination mode. In afirst illumination mode of FIG. 3C, aperture plate 13E provides off-axisillumination from a direction designated, for the sake of descriptiononly, as ‘east’ relative to the ‘north’ previously described. In asecond illumination mode of FIG. 3C, aperture plate 13W is used toprovide similar illumination, but from an opposite direction, labeled‘west’. FIG. 3D illustrates two further types of off-axis illuminationmode. In a first illumination mode of FIG. 3D, aperture plate 13NWprovides off-axis illumination from the directions designated ‘north’and ‘west’ as previously described. In a second illumination mode,aperture plate 13SE is used to provide similar illumination, but from anopposite direction, labeled ‘south’ and ‘east’ as previously described.The use of these, and numerous other variations and applications of theapparatus are described in, for example, the prior published patentapplication publications mentioned above.

FIG. 4 depicts an example composite metrology target T formed on asubstrate.

The composite target comprises four periodic structures (in this case,gratings) 32, 33, 34, 35 positioned closely together. In an embodiment,the periodic structure layout may be made smaller than the measurementspot (i.e., the periodic structure layout is overfilled). Thus, in anembodiment, the periodic structures are positioned closely togetherenough so that they all are within a measurement spot 31 formed by theillumination beam of the metrology apparatus. In that case, the fourperiodic structures thus are all simultaneously illuminated andsimultaneously imaged on sensors 19 and 23. In an example dedicated tooverlay measurement, periodic structures 32, 33, 34, 35 are themselvescomposite periodic structures (e.g., composite gratings) formed byoverlying periodic structures, i.e., periodic structures are patternedin different layers of the device formed on substrate W and such that atleast one periodic structure in one layer overlays at least one periodicstructure in a different layer. Such a target may have outer dimensionswithin 20 μm×20 μm or within 16 μm×16 μm. Further, all the periodicstructures are used to measure overlay between a particular pair oflayers. To facilitate a target being able to measure more than a singlepair of layers, periodic structures 32, 33, 34, 35 may have differentlybiased overlay offsets in order to facilitate measurement of overlaybetween different layers in which the different parts of the compositeperiodic structures are formed. Thus, all the periodic structures forthe target on the substrate would be used to measure one pair of layersand all the periodic structures for another same target on the substratewould be used to measure another pair of layers, wherein the differentbias facilitates distinguishing between the layer pairs.

Returning to FIG. 4, periodic structures 32, 33, 34, 35 may also differin their orientation, as shown, so as to diffract incoming radiation inX and Y directions. In one example, periodic structures 32 and 34 areX-direction periodic structures with biases of +d, −d, respectively.Periodic structures 33 and 35 may be Y-direction periodic structureswith offsets +d and −d respectively. While four periodic structures areillustrated, another embodiment may include a larger matrix to obtaindesired accuracy. For example, a 3×3 array of nine composite periodicstructures may have biases −4d, −3d, −2d, −d, 0, +d, +2d, +3d, +4d.Separate images of these periodic structures can be identified in animage captured by sensor 23.

FIG. 5 shows an example of an image that may be formed on and detectedby the sensor 23, using the target of FIG. 4 in the apparatus of FIG. 3,using the aperture plates 13NW or 13SE from FIG. 3D. While the sensor 19cannot resolve the different individual periodic structures 32 to 35,the sensor 23 can do so. The dark rectangle represents the field of theimage on the sensor, within which the illuminated spot 31 on thesubstrate is imaged into a corresponding circular area 41. Within this,rectangular areas 42-45 represent the images of the periodic structures32 to 35. The target can be positioned in among device product features,rather than or in addition to in a scribe lane. If the periodicstructures are located in device product areas, device features may alsobe visible in the periphery of this image field. Processor andcontroller PU processes these images using pattern recognition toidentify the separate images 42 to 45 of periodic structures 32 to 35.In this way, the images do not have to be aligned very precisely at aspecific location within the sensor frame, which greatly improvesthroughput of the measuring apparatus as a whole.

Once the separate images of the periodic structures have beenidentified, the intensities of those individual images can be measured,e.g., by averaging or summing selected pixel intensity values within theidentified areas. Intensities and/or other properties of the images canbe compared with one another. These results can be combined to measuredifferent parameters of the lithographic process. Overlay performance isan example of such a parameter.

In an embodiment, one of the parameters of interest of a patterningprocess is feature width (e.g., CD). FIG. 6 depicts a highly schematicexample metrology apparatus (e.g., a scatterometer) that can enablefeature width determination. It comprises a broadband (white light)radiation projector 2 which projects radiation onto a substrate W. Theredirected radiation is passed to a spectrometer detector 4, whichmeasures a spectrum 10 (intensity as a function of wavelength) of thespecular reflected radiation, as shown, e.g., in the graph in the lowerleft. From this data, the structure or profile giving rise to thedetected spectrum may be reconstructed by processor PU, e.g. by RigorousCoupled Wave Analysis and non-linear regression or by comparison with alibrary of simulated spectra as shown at the bottom right of FIG. 6. Ingeneral, for the reconstruction the general form of the structure isknown and some variables are assumed from knowledge of the process bywhich the structure was made, leaving only a few variables of thestructure to be determined from the measured data. Such a metrologyapparatus may be configured as a normal-incidence metrology apparatus oran oblique-incidence metrology apparatus. Moreover, in addition tomeasurement of a parameter by reconstruction, angle resolvedscatterometry is useful in the measurement of asymmetry of features inproduct and/or resist patterns. A particular application of asymmetrymeasurement is for the measurement of overlay, where the targetcomprises one set of periodic features superimposed on another. Theconcepts of asymmetry measurement in this manner are described, forexample, in U.S. patent application publication US2006-066855, which isincorporated herein in its entirety.

FIG. 7 illustrates an example of a metrology apparatus 100 suitable foruse in embodiments of the invention disclosed herein. The principles ofoperation of this type of metrology apparatus are explained in moredetail in the U.S. Patent Application Nos. US 2006-033921 and US2010-201963, which are incorporated herein in their entireties byreference. An optical axis, which has several branches throughout theapparatus, is represented by a dotted line O. In this apparatus,radiation emitted by source 110 (e.g., a xenon lamp) is directed ontosubstrate W via by an optical system comprising: lens system 120,aperture plate 130, lens system 140, a partially reflecting surface 150and objective lens 160. In an embodiment these lens systems 120, 140,160 are arranged in a double sequence of a 4F arrangement. In anembodiment, the radiation emitted by radiation source 110 is collimatedusing lens system 120. A different lens arrangement can be used, ifdesired. The angular range at which the radiation is incident on thesubstrate can be selected by defining a spatial intensity distributionin a plane that presents the spatial spectrum of the substrate plane. Inparticular, this can be done by inserting an aperture plate 130 ofsuitable form between lenses 120 and 140, in a plane which is aback-projected image of the objective lens pupil plane. Differentintensity distributions (e.g., annular, dipole, etc.) are possible byusing different apertures. The angular distribution of illumination inradial and peripheral directions, as well as properties such aswavelength, polarization and/or coherency of the radiation, can all beadjusted to obtain desired results. For example, one or moreinterference filters 130 (see FIG. 9) can be provided between source 110and partially reflecting surface 150 to select a wavelength of interestin the range of, say, 400-900 nm or even lower, such as 200-300 nm. Theinterference filter may be tunable rather than comprising a set ofdifferent filters. A grating could be used instead of an interferencefilter. In an embodiment, one or more polarizers 170 (see FIG. 9) can beprovided between source 110 and partially reflecting surface 150 toselect a polarization of interest. The polarizer may be tunable ratherthan comprising a set of different polarizers.

As shown in FIG. 7, the target T is placed with substrate W normal tothe optical axis O of objective lens 160. Thus, radiation from source110 is reflected by partially reflecting surface 150 and focused into anillumination spot S (see FIG. 8) on target T on substrate W viaobjective lens 160. In an embodiment, objective lens 160 has a highnumerical aperture (NA), desirably at least 0.9 or at least 0.95. Animmersion metrology apparatus (using a relatively high refractive indexfluid such as water) may even have a numerical aperture over 1.

Rays of illumination 170, 172 focused to the illumination spot fromangles off the axis O gives rise to diffracted rays 174, 176. It shouldbe remembered that these rays are just one of many parallel rayscovering an area of the substrate including target T. Each elementwithin the illumination spot is within the field of view of themetrology apparatus. Since the aperture in plate 130 has a finite width(necessary to admit a useful quantity of radiation), the incident rays170, 172 will in fact occupy a range of angles, and the diffracted rays174, 176 will be spread out somewhat. According to the point spreadfunction of a small target, each diffraction order will be furtherspread over a range of angles, not a single ideal ray as shown.

At least the 0^(th) order diffracted by the target on substrate W iscollected by objective lens 160 and directed back through partiallyreflecting surface 150. An optical element 180 provides at least part ofthe diffracted beams to optical system 182 which forms a diffractionspectrum (pupil plane image) of the target T on sensor 190 (e.g. a CCDor CMOS sensor) using the zeroth and/or first order diffractive beams.In an embodiment, an aperture 186 is provided to filter out certaindiffraction orders so that a particular diffraction order is provided tothe sensor 190. In an embodiment, the aperture 186 allows substantiallyor primarily only zeroth order radiation to reach the sensor 190. In anembodiment, the sensor 190 may be a two-dimensional detector so that atwo-dimensional angular scatter spectrum of a substrate target T can bemeasured. The sensor 190 may be, for example, an array of CCD or CMOSsensors, and may use an integration time of, for example, 40milliseconds per frame. The sensor 190 may be used to measure theintensity of redirected radiation at a single wavelength (or narrowwavelength range), the intensity separately at multiple wavelengths orintegrated over a wavelength range. Furthermore, the sensor may be usedto separately measure the intensity of radiation with transversemagnetic- and/or transverse electric-polarization and/or the phasedifference between transverse magnetic- and transverseelectric-polarized radiation.

Optionally, optical element 180 provides at least part of the diffractedbeams to measurement branch 200 to form an image of the target on thesubstrate W on a sensor 230 (e.g. a CCD or CMOS sensor). The measurementbranch 200 can be used for various auxiliary functions such as focusingthe metrology apparatus (i.e., enabling the substrate W to be in focuswith the objective 160), and/or for dark field imaging of the typementioned in the introduction.

In order to provide a customized field of view for different sizes andshapes of grating, an adjustable field stop 300 is provided within thelens system 140 on the path from source 110 to the objective lens 160.The field stop 300 contains an aperture 302 and is located in a planeconjugate with the plane of the target T, so that the illumination spotbecomes an image of the aperture 302. The image may be scaled accordingto a magnification factor, or the aperture and illumination spot may bein 1:1 size relation. In order to make the illumination adaptable todifferent types of measurement, the aperture plate 300 may comprise anumber of aperture patterns formed around a disc, which rotates to bringa desired pattern into place. Alternatively or in addition, a set ofplates 300 could be provided and swapped, to achieve the same effect.Additionally or alternatively, a programmable aperture device such as adeformable mirror array or transmissive spatial light modulator can beused also.

Typically, a target will be aligned with its periodic structure featuresrunning either parallel to the Y axis or parallel to the X axis. Withregard to its diffractive behavior, a periodic structure with featuresextending in a direction parallel to the Y axis has periodicity in the Xdirection, while the a periodic structure with features extending in adirection parallel to the X axis has periodicity in the Y direction. Inorder to measure the performance in both directions, both types offeatures are generally provided. While for simplicity there will bereference to lines and spaces, the periodic structure need not be formedof lines and space. Moreover, each line and/or space between lines maybe a structure formed of smaller sub-structures. Further, the periodicstructure may be formed with periodicity in two dimensions at once, forexample where the periodic structure comprises posts and/or via holes.

FIG. 8 illustrates a plan view of a typical target T, and the extent ofillumination spot S in the apparatus of FIG. 7. To obtain a diffractionspectrum that is free of interference from surrounding structures, thetarget T, in an embodiment, is a periodic structure (e.g., grating)larger than the width (e.g., diameter) of the illumination spot S. Thewidth of spot S may be smaller than the width and length of the target.The target in other words is ‘underfilled’ by the illumination, and thediffraction signal is essentially free from any signals from productfeatures and the like outside the target itself. This simplifiesmathematical reconstruction of the target as it can be regarded asinfinite.

FIG. 9 schematically depicts an example process of the determination ofthe value of one or more variables of interest of a target pattern 30′based on measurement data obtained using metrology. Radiation detectedby the detector 190 provides a measured radiation distribution 108 fortarget 30′.

For the given target 30′, a radiation distribution 208 can becomputed/simulated from a parameterized mathematical model 206 using,for example, a numerical Maxwell solver 210. The parameterizedmathematical model 206 shows example layers of various materials makingup, and associated with, the target. The parameterized mathematicalmodel 206 may include one or more of variables for the features andlayers of the portion of the target under consideration, which may bevaried and derived. As shown in FIG. 9, the one or more of the variablesmay include the thickness t of one or more layers, a width w (e.g., CD)of one or more features, a height h of one or more features, a sidewallangle a of one or more features, and/or relative position betweenfeatures (herein considered overlay). Although not shown, the one ormore of the variables may further include, but is not limited to, therefractive index (e.g., a real or complex refractive index, refractiveindex tensor, etc.) of one or more of the layers, the extinctioncoefficient of one or more layers, the absorption of one or more layers,resist loss during development, a footing of one or more features,and/or line edge roughness of one or more features. One or more valuesof one or more parameters of a 1-D periodic structure or a 2-D periodicstructure, such as a value of width, length, shape or a 3-D profilecharacteristic, may be input to the reconstruction process fromknowledge of the patterning process and/or other measurement processes.For example, the initial values of the variables may be those expectedvalues of one or more parameters, such as a value of CD, pitch, etc.,for the target being measured.

In some cases, a target can be divided into a plurality of instances ofa unit cell. To help ease computation of the radiation distribution of atarget in that case, the model 206 can be designed to compute/simulateusing the unit cell of the structure of the target, where the unit cellis repeated as instances across the full target. Thus, the model 206 cancompute using one unit cell and copy the results to fit a whole targetusing appropriate boundary conditions in order to determine theradiation distribution of the target.

Additionally or alternatively to computing the radiation distribution208 at the time of reconstruction, a plurality of radiationdistributions 208 can be pre-computed for a plurality of variations ofvariables of the target portion under consideration to create a libraryof radiation distributions for use at the time of reconstruction.

The measured radiation distribution 108 is then compared at 212 to thecomputed radiation distribution 208 (e.g., computed near that time orobtained from a library) to determine the difference between the two. Ifthere is a difference, the values of one or more of the variables of theparameterized mathematical model 206 may be varied, a new computedradiation distribution 208 obtained (e.g., calculated or obtained from alibrary) and compared against the measured radiation distribution 108until there is sufficient match between the measured radiationdistribution 108 and the radiation distribution 208. At that point, thevalues of the variables of the parameterized mathematical model 206provide a good or best match of the geometry of the actual target 30′.In an embodiment, there is sufficient match when a difference betweenthe measured radiation distribution 108 and the computed radiationdistribution 208 is within a tolerance threshold.

In these metrology apparatuses, a substrate support may be provided tohold the substrate W during measurement operations. The substratesupport may be similar or identical in form to the substrate table WT ofFIG. 1. In an example where the metrology apparatus is integrated withthe lithographic apparatus, it may even be the same substrate table.Coarse and fine positioners may be provided to accurately position thesubstrate in relation to a measurement optical system. Various sensorsand actuators are provided for example to acquire the position of atarget of interest, and to bring it into position under the objectivelens. Typically many measurements will be made on targets at differentlocations across the substrate W. The substrate support can be moved inX and Y directions to acquire different targets, and in the Z directionto obtain a desired location of the target relative to the focus of theoptical system. It is convenient to think and describe operations as ifthe objective lens is being brought to different locations relative tothe substrate, when, for example, in practice the optical system mayremain substantially stationary (typically in the X and Y directions,but perhaps also in the Z direction) and only the substrate moves.Provided the relative position of the substrate and the optical systemis correct, it does not matter in principle which one of those is movingin the real world, or if both are moving, or a combination of a part ofthe optical system is moving (e.g., in the Z and/or tilt direction) withthe remainder of the optical system being stationary and the substrateis moving (e.g., in the X and Y directions, but also optionally in the Zand/or tilt direction).

In an embodiment, the measurement accuracy and/or sensitivity of atarget may vary with respect to one or more attributes of the beam ofradiation provided onto the target, for example, the wavelength of theradiation beam, the polarization of the radiation beam, the intensitydistribution (i.e., angular or spatial intensity distribution) of theradiation beam, etc. Thus, a particular measurement strategy can beselected that desirably obtains, e.g., good measurement accuracy and/orsensitivity of the target.

In order to monitor the patterning process (e.g., a device manufacturingprocess) that includes at least one pattern transfer step (e.g., anoptical lithography step), the patterned substrate is inspected and oneor more parameters of the patterned substrate are measured/determined.The one or more parameters may include, for example, overlay betweensuccessive layers formed in or on the patterned substrate, criticaldimension (CD) (e.g., critical linewidth) of, for example, featuresformed in or on the patterned substrate, focus or focus error of anoptical lithography step, dose or dose error of an optical lithographystep, optical aberrations of an optical lithography step, placementerror (e.g., edge placement error), etc. This measurement may beperformed on a target of the product substrate itself and/or on adedicated metrology target provided on the substrate. The measurementcan be performed after-development of a resist but before etching or canbe performed after-etch.

In an embodiment, a parameter obtained from a measurement process is aparameter derived from a parameter determined directly from themeasurement process. As an example, a derived parameter obtained from ameasurement parameter is edge placement error for the patterningprocess. The edge placement error provides a variation in the locationof an edge of a structure created by the patterning process. In anembodiment, the edge placement error is derived from an overlay value.In an embodiment, the edge placement error is derived from a combinationof an overlay value and CD value. In an embodiment, the edge placementis derived from a combination of an overlay value, a CD value and avalue corresponding to a local variation (e.g., edge roughness, shapeasymmetry, etc. of the individual structures). In an embodiment, theedge placement error comprises an extreme value (e.g., 3 standarddeviation, i.e., 3 a) of overlay and CD errors combined. In anembodiment, in a multi-patterning process involving creating structuresand involving “cutting” structures by removing a portion of structurethrough etching of a pattern provided by the patterning process inrelation to the structure, the edge placement error has the followingform (or comprises one or more of the following terms):

${\sqrt{\frac{\left( {3\; \sigma_{overlay}} \right)^{2} + \left( \frac{3\sigma_{{CDU}\; {structures}}}{2} \right)^{2} +}{\left( \frac{3\; \sigma_{{CDU}\; {cuts}}}{2} \right)^{2}}} + \frac{3\; \sigma_{{OPE},{PBA}}}{2} + {6\; \sigma_{{LER},{LPE}}}},$

wherein σ is standard deviation, σ_(overlay) corresponds to the standarddeviation of overlay, corresponds to the standard deviation of overlay,σ_(CDU structures) corresponds to the standard deviation of the criticaldimension uniformity (CDU) of structures created in the patterningprocess, σ_(CDU cuts) corresponds to the standard deviation of thecritical dimension uniformity (CDU) of cuts, if any, created in thepatterning process, σ_(OPE,PBA) corresponds to the standard deviation ofoptical proximity effects (OPE) and/or proximity bias average (PBA)which is a difference between CD at pitch to a reference CD, andσ_(LER,LPE) corresponds to the standard deviation of line edge roughness(LER) and/or local placement error (LPE). While formulation above is inrelation standard deviation, it can be formulated in a differentcomparable statistical manner, such as variance.

There are various techniques for making measurements of the structuresformed in the patterning process, including the use of a scanningelectron microscope, an image-based measurement tool and/or variousspecialized tools. As discussed above, a fast and non-invasive form ofspecialized metrology tool is one in which a beam of radiation isdirected onto a target on the surface of the substrate and properties ofthe scattered (diffracted/reflected) beam are measured. By evaluatingone or more properties of the radiation scattered by the substrate, oneor more properties of the substrate can be determined. This may betermed diffraction-based metrology. One such application of thisdiffraction-based metrology is in the measurement of feature asymmetrywithin a target. This can be used as a measure of overlay, for example,but other applications are also known. For example, asymmetry can bemeasured by comparing opposite parts of the diffraction spectrum (forexample, comparing the −1st and +1^(st) orders in the diffractionspectrum of a periodic grating). This can be done as described above andas described, for example, in U.S. patent application publicationUS2006-066855, which is incorporated herein in its entirety byreference. Another application of diffraction-based metrology is in themeasurement of feature width (CD) within a target. Such techniques canuse the apparatus and methods described above in respect of FIGS. 6-9.

Now, while these techniques are effective, it is desirable to provide anew measurement technique that derives feature asymmetry within a target(such as overlay, CD asymmetry, sidewall angle asymmetry, etc.). Thistechnique can be effective for specially designed metrology targets orperhaps more significantly, for determining feature asymmetry directlyon a device pattern.

Referring to FIG. 10, principles of this measurement technique aredescribed in the context of an overlay embodiment. In FIG. 10A, ageometrically symmetric unit cell of a target T is shown. The target Tcan comprise just a single physical instance of a unit cell or cancomprise a plurality of physical instances of the unit cell as shown inFIG. 10C.

The target T can be a specially designed target. In an embodiment, thetarget is for a scribe lane. In an embodiment, the target can be anin-die target, i.e., the target is among the device pattern (and thusbetween the scribe lanes). In an embodiment, the target can have afeature width or pitch comparable to device pattern features. Forexample, the target feature width or pitches can be less than or equalto 300% of the smallest feature size or pitch of the device pattern, beless than or equal to 200% of the smallest feature size or pitch of thedevice pattern, be less than or equal to 150% of the smallest featuresize or pitch of the device pattern, or be less than or equal to 100% ofthe smallest feature size or pitch of the device pattern.

The target T can be a device structure. For example, the target T can bea portion of a memory device (which often has one or more structuresthat are, or can be, geometrically symmetric as discussed furtherbelow).

In an embodiment, the target T or a physical instance of the unit cellcan have an area of less than or equal to 2400 square microns, an areaof less than or equal to 2000 square microns, an area of less than orequal to 1500 square microns, an area of less than or equal to 1000square microns, an area of less than or equal to 400 square microns,less than or equal to 200 square microns, less than or equal to 100square microns, less than or equal to 50 square microns, less than orequal to 25 square microns, less than or equal to 10 square microns,less than or equal to 5 square microns, less than or equal to 1 squaremicron, less than or equal to 0.5 square microns, or less than or equalto 0.1 square microns. In an embodiment, the target T or a physicalinstance of the unit cell has a cross-sectional dimension parallel tothe plane of the substrate of less than or equal to 50 microns, lessthan or equal to 30 microns, less than or equal to 20 microns, less thanor equal to 15 microns, less than or equal to 10 microns, less than orequal to 5 microns, less than or equal to 3 microns, less than or equalto 1 micron, less than or equal to 0.5 microns, less than or equal to0.2 microns, or less than or equal to 0.1 microns.

In an embodiment, the target T or a physical instance of the unit cellhas a pitch of structures of less than or equal to less than or equal to5 microns, less than or equal to 2 microns, less than or equal to 1micron, less than or equal to 500 nm, less than or equal to 400 nm, lessthan or equal to 300 nm, less than or equal to 200 nm, less than orequal to 150 nm, less than or equal to 100 nm, less than or equal to 75nm, less than or equal to 50 nm, less than or equal to 32 nm, less thanor equal to 22 nm, less than or equal to 16 nm, less than or equal to 10nm, less than or equal to 7 nm or less than or equal to 5 nm.

In an embodiment, the target T has a plurality of physical instances ofthe unit cell. Thus, a target T could typically have the higherdimensions listed here, while the physical instances of the unit cellwill have the lower dimensions listed here. In an embodiment, the targetT comprises 50,000 or more physical instances of the unit cell, 25,000or more physical instances of the unit cell, 15,000 or more physicalinstances of the unit cell, 10,000 or more physical instances of theunit cell, 5,000 or more physical instances of the unit cell, 1000 ormore physical instances of the unit cell, 500 or more physical instancesof the unit cell, 200 or more physical instances of the unit cell, 100or more physical instances of the unit cell, 50 or more physicalinstances of the unit cell, or 10 or more physical instances of the unitcell.

Desirably, the physical instance of the unit cell or the plurality ofphysical instances of the unit cell collectively fills a beam spot ofthe metrology apparatus. In that case, the measured results compriseessentially only information from the physical instance of the unit cell(or its plurality of instances). In an embodiment, the beam spot has across-sectional width of 50 microns or less, 40 microns or less, 30microns or less, 20 microns or less, 15 microns or less, 10 microns orless, 5 microns or less, or 2 microns or less.

The unit cell in FIG. 10A comprises at least two structures that are, orwill be, physically instantiated on the substrate. A first structure1000 comprises lines and a second structure 1005 comprises an oval-typeshape. Of course, the first and second structures 1000, 1005 can bedifferent structures than depicted.

Further, in this example, there can be a relative shift between thefirst and second structures 1000, 1005 from their expected position dueto their separate transfer onto the substrate so as to have an error inoverlay. In this example, the first structure 1000 is located in ahigher layer on a substrate than the second structure 1005. Thus, in anembodiment, the second structure 1005 can be produced in a first lowerlayer in a first execution of a patterning process and the firststructure 1000 can be produced in a second higher layer than the firstlower layer in a second execution of the patterning process. Now, it isnot necessary that the first and second structures 1000, 1005 be locatedin different layers. For example, in a double patterning process(including, for example, an etching process as part thereof), the firstand second structures 1000, 1005 could be produced in a same layer toform essentially a single pattern but there could still be an “overlay”concern in terms of their relative placement within the same layer. Inthis single layer example, both the first and second structures 1000,1005 could have, for example, the form of lines like shown in FIG. 10Afor the first structure 1000 but the lines of the second structure 1005,already provided on the substrate by a first pattern transfer process,could be interleaved with the lines of the structure 1000 provided in asecond pattern transfer process.

Significantly, the unit cell has, or is capable of having, a geometricsymmetry with respect to an axis or point. For example, the unit cell inFIG. 10A has reflection symmetry with respect to, for example, axis 1010and point/rotational symmetry with respect to, for example, point 1015.Similarly, it can be seen that a physical instance of the unit cell (andthus a combination of physical instances of the unit cell) in FIG. 10Chas a geometric symmetry.

In an embodiment, the unit cell has a geometric symmetry for a certainfeature (such as overlay). Embodiments herein focus on the unit cellhaving zero overlay when it is geometrically symmetric. However,instead, the unit cell can have zero overlay for a certain geometricasymmetry. Appropriate offsets and calculations would then be used toaccount for the unit cell having a zero overlay when it has a certaingeometric asymmetry. Pertinently, the unit cell should be capable ofchange in symmetry (e.g., become asymmetry, or become furtherasymmetric, or become symmetric from an asymmetric situation) dependingon the certain feature value.

In the example of FIG. 10A, the unit cell has a geometric symmetry for azero overlay (although it need not be zero overlay). This is representedby the arrows 1020 and 1025 which shows that the lines of the firststructure 1000 are evenly aligned with respect to the oval-type shape ofthe second structure 1005 (and which even alignment at least in partenables the unit cell to have geometric symmetry as shown in FIG. 10A).So, in this example, when the unit cell has geometric symmetry, there iszero overlay. However, when there is an error in overlay (e.g., anon-zero overlay), the unit cell is no longer geometrically symmetricand by definition the target is no longer geometrically symmetric.

Further, where a target comprises a plurality of physical instances ofthe unit, the instances of the unit cell are arranged periodically. Inan embodiment, the instances of the unit cell are arranged in a lattice.In an embodiment, the periodic arrangement has a geometric symmetrywithin the target.

So, in this technique, as discussed further hereafter, advantage istaken of the change in geometric symmetry (e.g., a change to a geometricasymmetry, or change to a further geometric asymmetry, or a change fromgeometric asymmetry to geometric symmetry) related to a featureasymmetry of interest (e.g., non-zero overlay) to be able to determinethe feature asymmetry (e.g., non-zero overlay).

A target comprising a physical instance of the unit cell of FIG. 10A canbe illuminated with radiation using, for example, the metrologyapparatus of FIG. 7. The radiation redirected by the target can bemeasured, e.g., by detector 190. In an embodiment, a pupil of theredirected radiation is measured, i.e., a Fourier transform plane. Anexample measurement of such a pupil is depicted as pupil image 1030.While the pupil image 1030 has a diamond-type shape, it need not havesuch a shape. The term pupil and pupil plane herein includes anyconjugates thereof unless the context otherwise requires (for example,where a pupil plane of a particular optical system is being identified).The pupil image 1030 is effectively an image, specified in terms of anoptical characteristic (in this case intensity), of a pupil of theredirected radiation.

For convenience, the discussion herein will focus on intensity as anoptical characteristic of interest. But, the techniques herein may beused with one or more alternative or additional optical characteristics,such as phase and/or reflectivity.

Further, for convenience, the discussion herein focuses on detecting andprocessing images of redirected radiation and in particular pupilimages. However, the optical properties of the redirected radiation canbe measured and represented in different manners than images. Forexample, the redirected radiation can be processed in terms of one ormore spectrums (e.g., intensity as a function of wavelength). Thus, adetected image of redirected radiation can be considered as an exampleof an optical representation of the redirected radiation. So, in thecase of a pupil plane image, a pupil image is an example of a pupilrepresentation.

Further, the redirected radiation can be polarized or non-polarized. Inan embodiment, the measurement beam radiation is polarized radiation. Inan embodiment, the measurement beam radiation is linearly polarized.

In an embodiment, a pupil representation is of primarily, orsubstantially, one diffraction order of redirected radiation from thetarget. For example, the radiation can be 80% or more, 85% or more, 90%or more, 95% or more, 98% or more or 99% or more, of a particular orderof the radiation. In an embodiment, the pupil representation is ofprimarily, or substantially, zeroth order redirected radiation. This canoccur, for example, when the pitch of the target, the wavelength of themeasurement radiation, and optionally one or more other conditions causethe target to redirect primarily zeroth order (although there can beradiation of one or more higher orders). In an embodiment, a majority ofthe pupil representation is zeroth order redirected radiation. In anembodiment, the pupil representation is of zeroth radiation andseparately of 1st order radiation, which can then be linearly combined(superposition). The aperture 186 in FIG. 7 can be used to select aparticular order, e.g., the zeroth order, of radiation.

Having regard to pupil image 1030 corresponding to the geometricallysymmetric unit cell of the first and second structures 1000, 1005, itcan be seen that the intensity distribution is essentially symmetricwithin the pupil image (e.g., with the same symmetry type as of thegeometric structure). This is further confirmed by removing thesymmetric intensity distribution portion from the pupil image 1030,which results in the derived pupil image 1035. To remove the symmetricintensity distribution portion, a particular pupil image pixel (e.g., apixel) can have the symmetric intensity distribution portion removed bysubtracting from the intensity at that particular pupil image pixel theintensity of a symmetrically located pupil image pixel, and vice versa.In an embodiment, the pixel can correspond to the pixels of the detector(e.g., detector 190), but it need not; for example, a pupil image pixelcould be a plurality of the pixels of the detector. In an embodiment,the point or axis of symmetry across which pixel intensities aresubtracted corresponds with a point or axis of symmetry of the unitcell. So, for example, considering pupil image 1030, the symmetryintensity distribution portion can be removed by, for example,subtracting from the intensity I_(i) at that particular pixel shown theintensity I_(i)′ from a symmetrically located pixel, i.e., symmetricallylocated with respect to axis 1032. Thus, the intensity at a particularpixel with the symmetrical intensity portion removed, S_(i), is thenS_(i)=I_(i)−I_(i)′. This can be repeated for a plurality of pixels ofthe pupil image, e.g., all the pixels in the pupil image. As seen in thederived pupil image 1035, the intensity distribution corresponding tothe symmetric unit cell is essentially completely symmetric. Thus, asymmetric target with a symmetric unit cell geometry (and if applicable,a certain periodicity of instances of the unit cell) results in asymmetric pupil response as measured by a metrology apparatus.

Referring now to FIG. 10B, an example of an error in overlay is depictedwith respect to the unit cell depicted in FIG. 10A. In this case, thefirst structure 1000 is shifted in the X-direction with respect to thesecond structure 1005. In particular, the axis 1010 centered on thelines of the first structure 1000 has shifted to the right in FIG. 10Bto axis 1045. Thus, there is an error in the overlay 1040 in theX-direction; that is, an X direction overlay error. Of course, thesecond structure 1005 could be shifted relative to the first structure1000 or both could be shifted relative to each other. In any event, theresult is an X direction overlay error. However, as should beappreciated from this unit cell arrangement, a purely relative shift inthe Y-direction between the first structure 1000 and the secondstructure 1005 would not change the geometric symmetry of this unitcell. But, with an appropriate geometric arrangement, overlay in twodirections or between different combinations of parts of the unit cellcan change symmetry and could also be determined, as further discussedbelow.

As a consequence of the change in the physical configuration of the unitcell from the nominal physical configuration of the unit cell in FIG.10A and represented by the error in overlay 1040, the result is that theunit cell has become geometrically asymmetric. This can be seen by thearrows 1050 and 1055 of different length, which show that the oval-typeshape of the second structure 1005 is unevenly located relative to thelines of the first structure 1000. The symmetry is examined with respectto the point or axis of symmetry of the pupil image 1030, i.e. in thatcase, axis 1032 which is now shown axis 1034.

The physical instance of the unit cell of FIG. 10B can be illuminatedwith radiation using, for example, the metrology apparatus of FIG. 7. Apupil image of the redirected radiation can be recorded, e.g., bydetector 190. An example of such a pupil image is depicted as pupilimage 1060. The pupil image 1060 is effectively an image of theintensity. While the pupil image 1060 has a diamond-type shape, it neednot have such a shape; it can be a circular shape or any other shape.Moreover, the pupil image 1060 is of a substantially same axis orcoordinate location as pupil image 1030. That is, in this embodiment, anaxis of symmetry 1010 in the unit cell of FIG. 10A and the same axis inthe unit cell of FIG. 10B align with an axis of symmetry 1032 of thepupil images 1030, 1060.

Having regard to pupil image 1060 corresponding to the geometricallyasymmetric unit cell of the first and second structures 1000, 1005, itvisually seems like the intensity distribution is essentially symmetricwithin the pupil image. However, there is an asymmetric intensitydistribution portion within the pupil image. This asymmetric intensitydistribution portion is due to the asymmetry in the unit cell. Moreover,the asymmetric intensity distribution is significantly lower inmagnitude than a symmetric intensity distribution portion in the pupilimage.

So, in an embodiment, to more effectively isolate the asymmetricintensity distribution portion, the symmetric intensity distributionportion can be removed from the pupil image 1060, which results in thederived pupil image 1065. Like with obtaining derived pupil image 1035,a particular pupil image pixel (e.g., a pixel) can have the symmetricintensity distribution portion removed by subtracting from the intensityat that particular pupil image pixel the intensity of a symmetricallylocated pupil image pixel, and vice versa, as discussed above. So, forexample, considering pupil image 1060, the symmetry intensitydistribution portion can be removed by, for example, subtracting fromthe intensity I_(i) at that particular pixel shown the intensity I_(i)′from a symmetrically located pixel, i.e., symmetrically located withrespect to axis 1032 to yield S_(i). This can be repeated for aplurality of pixels of the pupil image, e.g., all the pixels in thepupil image. In FIGS. 10A and 10B, the full derived pupil images ofS_(i) are depicted for explanation purposes. As will be appreciated,half of a derived pupil image of FIG. 10A or 10B is the same as theother half thereof. So, in an embodiment, the values from only half ofthe pupil image can be used for further processing discussed herein andso a derived image pupil used in further processing herein can be onlyhalf of the S_(i), values for a pupil.

As seen in the derived pupil image 1065, the intensity distributionmeasured using a physical instance of an asymmetric unit cell is notsymmetric. As seen in regions 1075 and 1080, there is an asymmetricintensity distribution portion visible once the symmetric intensitydistribution portion is removed. As noted above, the full derived pupilimage 1065 is shown and so the asymmetric intensity distribution portionis shown on both halves (even though they are equal to each other interms of magnitude and distribution in their respective halves).

Thus, an asymmetry in the geometrical domain corresponds to an asymmetryin the pupil. So, in an embodiment, a method is provided that uses theoptical response of a periodic target that possesses, or is capable of,inherent geometric symmetry in its physical instance of a unit cell todetermine a parameter corresponding to a physical configuration changethat causes a change in geometric symmetry (e.g., cause an asymmetry, orcause a further asymmetry, or cause an asymmetric unit cell to becomesymmetric) of the physical instance of the unit cell. In particular, inan embodiment, an overlay induced asymmetry (or lack thereof) in thepupil as measured by a metrology apparatus can be exploited to determinethe overlay. That is, the pupil asymmetry is used to measure the overlaywithin the physical instance of the unit cell and thus within thetarget.

To consider how to determine the parameter corresponding to a physicalconfiguration change that causes a geometric asymmetry in a unit cell,the intensity of a pixel in the pupil image can be considered in termsof the physical characteristics of the target that impact that pixel. Todo so, an overlay example will be considered but the techniques andprinciples can be extended to another parameter corresponding to aphysical configuration change that causes a geometric asymmetry in aunit cell (e.g., asymmetric sidewall angle, asymmetric bottom wall tilt,ellipticity in contact holes, etc.).

Referring back to the unit cells of FIGS. 10A and 10B, the intensity ofa pixel I_(i),I′_(i) in the pupil image 1060 can be evaluatedanalytically as a combination of intensity components attributable todifferent physical characteristics of the unit cell. In particular, thephysical configuration changes from the symmetric unit cell to theasymmetric unit cell can be evaluated to determine in what manner theintensity distribution changes and specifically within a pupil image.

So, in a very simple example to illustrate the principles, severalchanges in physical configuration of the unit cell profile can beevaluated (but of course more or different physical configurationchanges can occur). One of the physical configuration changes that willbe considered is the change in height of the structure 1000 in the Zdirection, which is designated as Δx_(h). But, significantly, thischange in height will generally be uniform across the physical instanceof the unit cell. That is, the Δx_(h) will result in a same changedphysical configuration of the unit cell at one side of an axis or pointof symmetry as at another side of the axis or point of symmetry.Similarly, other physical configuration changes, such as CD, sidewallangle, etc. changes, will also be generally uniform across the physicalinstance of the unit cell and thus yield a same changed physicalconfiguration of the unit cell at one side of an axis or point ofsymmetry as at another side of the axis or point of symmetry. So, forconvenience, only Δx_(h) will be considered, but is representative ofnumerous other physical configuration changes that are uniform acrossthe unit cell.

Another one of the physical configuration changes of the unit cell ofinterest is the relative shift between structure 1000 and structure1005, namely the change in overlay 1040. This overlay shift will bereferred to as Δx_(ov). Of course, the overlay can be considered in adifferent or additional direction. Significantly, the Δx_(ov) willresult in a different physical configuration of the unit cell at oneside of an axis or point of symmetry than at another side of the axis orpoint of symmetry; each pair of symmetric pixels has information aboutoverlay. Significantly, while change in most target profile parameters(CD, height, etc.) induce symmetric changes in the pupil (and thus canbe considered symmetric parameters), change in overlay results in anasymmetric change in the measured pupil. Thus, a change in overlay givesan asymmetric pupil response. Further, most, if not all, other unit cellprofile parameters do not create asymmetry of the unit cell or the pupilresponse. However, they can have an effect on the measured overlayvalue. As discussed below, to the first order, other unit cell profileparameters may have no effect. In an embodiment, to a second or higherorder, other unit cell profile parameters have an effect ondetermination of the overlay value. Hence, as discussed in more detailbelow, by measuring the pupil asymmetry, overlay can be determinedtherefrom.

Specifically, to evaluate how overlay can be determined from a measuredpupil asymmetry, the intensity I_(i) of a pixel i in the pupil image1060 can be defined as:

I _(i) =I ₀ +aΔx _(ov) +dΔx _(h) +bΔx _(ov) Δx _(h) +eΔx _(ov) ² +fΔx_(h) ² + . . . cΔx _(ov) ³+ . . .  (1)

where I₀ is a base intensity attributable to the illumination radiationand a, e, f and g are coefficients. So, similarly, the intensity of thecomplementary symmetric pixel I′_(i) in the pupil image 1060 can bedefined as:

I′ _(i) =I ₀ +a′Δx _(ov) +d′Δx _(h) +b′x _(ov) Δx _(h) +e′Δx _(ov) ²+fΔx _(h) ² + . . . c′Δx _(ov) ³+ . . .  (2)

where coefficients a′, b′, c, d′, e′ and f′ are specific to theintensity of the complementary symmetric pixel and are comparable to thecoefficients a, b, c, d, e and f for the intensity of a pixel I_(i) inthe pupil image 1060.

The difference of the intensity S_(i)=I_(i)−I_(i)′ between the symmetricpixels in the pupil image 1060 can then be evaluated as:

S _(i) =I _(i) −I _(i)′=(a−a′)Δx _(ov)+(b−b′)Δx _(oc) Δx _(h)+(c−c′)Δx_(ov) ³+ . . .  (3)

It has been discovered that due to, e.g., symmetry, all the terms thatcan contain only symmetric parameters, such as eΔx_(h), drop out as seenin equation (3). Further, due to, e.g., symmetry, the terms with an evenpower of overlay have been discovered to be equal for symmetricallypositioned pixels and so terms such Δx_(ov) ² likewise drop out. Thatleaves, terms that have a combination of overlay with a symmetricparameter and terms that have only overlay to an odd power (e.g., to thepower of 1, 3, 5, 7, etc.).

In equation (3) above, it has been discovered that the difference of theintensity S_(i) is primarily dependent on aΔx_(ov). That is, thedifference of the intensity S_(i) is in great part linearly dependent onoverlay or more significantly, overlay is in great part linearlydependent on the intensity, specifically the difference of the intensityS_(i). Thus, a combination of the intensities of the pixels can yield agood estimated value of the overlay when linearly combined with anappropriate conversion factor.

So, in an embodiment, it has been discovered that an overlay can bedetermined from a combination of intensities of the pixels that areappropriately weighted (wherein the weighting themselves acts aconversion factor of intensity to overlay or that can be combined with aconversion factor from intensity to overlay). In an embodiment, anoverlay signal can be described as:

M=Σ _(i) w _(i) S _(i)  (4)

wherein the overlay signal M is the weighted combination of the signalcomponents S_(i) in the measured pupil and w_(i) are the respectiveweights for each of the signal components S_(i) (and the weights act asa conversion factor between the signal component and overlay; as notedabove, instead, a conversion factor could be used in combination withweights that do not act to convert the signal component to overlay). Inan embodiment, the weights w_(i) are a vector whose magnitude is relatedto the overlay. As noted above, the signal components S_(i) can bedetermined for half of the measured pupil. In an embodiment, if thesignal components S_(i) have a substantially same magnitude for allpairs (N/2) of symmetric pixels (N), then the signal components S_(i)can be averaged and combined with a conversion factor C from the totalof the signal components S_(i) to overlay according to the followingformula to yield a total overlay:

$M = {C\frac{2}{N}{\sum_{i}^{N/2}{S_{i}.}}}$

So, in an embodiment, the weights can have two roles—one is as a trustper pair of pixels in respect of its measurement of overlay and theother role is to convert a value of the optical characteristic of thesignal component (e.g., intensity level, e.g., gray level) to an overlayvalue (in terms of, e.g., nanometers), As discussed above, the secondrole can be delegated to a conversion factor.

But, where, e.g., the signal components S_(i) do not have asubstantially same magnitude for all pairs of symmetric pixels,weighting all pixels in the measured pupil equally could result in a lowsignal-to-noise ratio (poor precision). So, it is desirable to weightthose pixels that are sensitive to overlay to have a greatercontribution to the calculation of the overlay. So, in an embodiment,pixels sensitive to overlay get different (e.g., higher) weights thanthose pixels that have low sensitivity to overlay (effectively inactivepixels). As noted above, the pixels in regions 1075 and 1080 of thederived pupil 1065 have relatively higher sensitivity to overlay whilethe remaining pixels in the derived pupil 1065, which have low to nointensity relative to the pixels in regions 1075 and 1080, have lowsensitivity to overlay (and accordingly should be weighted to have lowercontribution to the overlay determination).

In an embodiment, the weights are effectively determined for theaΔx_(ov) term of equation (3). In an embodiment, the weights can beextended to be determined for the aΔx_(ov) term as well as thebΔx_(ov)Δx_(h)(and typically other comparable terms for otherparameters, such as CD, sidewall angle, etc.). However, this calculationcan be more complex than determining the weights effectively only forthe aΔx_(ov) term of equation (3). Moreover, there is a tradeoff betweenrobustness to non-linear processes (for symmetric parameters) andprecision of determining overlay (i.e., in terms of how close thedetermined values are for each determination of the same actualoverlay). So, there can be a sacrifice of precision for enhancedrobustness using this calculation. Accordingly, an optimization can beperformed to enhance precision (e.g., maximizing the influence of thelinear terms and suppressing the non-linear terms), enhance robustness(e.g., maximizing the non-linear terms) or find a balance of both. But,in any event, the use of a combination of intensities linearly combinedwith associated weightings can lead to a quick determination of overlayas it requires merely a pupil acquisition and simple calculation ofequation (4).

In an embodiment, where higher order terms become significant, anon-linear solution technique can be adopted to solve equation (3)having the cΔx_(ov) ³ and/or other higher order terms. As will beappreciated, a non-linear solution technique can be more complex thansimply multiplying each signal components S_(i) in the measured pupilwith a respective weight w_(i) for each signal components S_(i) and thenadding all of them up. Moreover, there is again tradeoff betweenrobustness to non-linear processes and precision of determining overlay(i.e., in terms of how close the determined values are for eachdetermination of the same actual overlay). So, there can be a sacrificeof precision for enhanced robustness using this calculation.Accordingly, an optimization can be performed to enhance precisionand/or enhance robustness.

So, with the realization of an asymmetric intensity distribution arisingfrom a geometric asymmetry of a unit cell caused by overlay, the errorin overlay can be determined through an analysis that has a focus onthis asymmetric intensity distribution. Thus, a technique fordetermining overlay from the asymmetric intensity distribution arisingdue to the change in physical configuration of a target associated withoverlay will now be discussed.

Referring to FIG. 11, a method of determining the weights isschematically depicted. To enable the weight determination, thereconstruction techniques described above with respect to FIG. 9 will beused to advantage. That is, in an embodiment, CD reconstruction is usedto isolate an overlay signal from a pupil image of an physical instanceof an asymmetric unit cell.

The method of FIG. 11 involves two processes. A first process 1100involves using reconstruction techniques for CD and/or one or more otherprofile parameters of a target to derive a nominal profile of the target(and thus of the one or more physical instances of the unit celltherein) as exposed on a substrate as part of a patterning process. Withthe nominal profile of the target, the basic engine of thereconstruction technique is used in process 1110 to derive theweightings. The weightings can then be used to derive overlay from ameasured pupil as described further in relation to FIG. 12.

So, at process 1100, measurements 1130 of a substrate having one or morephysical instances of a unit cell of interest provided thereon as atarget, are obtained. In an embodiment, the measurements are of thetarget after etch. In an embodiment, the measurements are of the targetafter development but before etch. In an embodiment, the target is adevice structure. In an embodiment, the measurements can be made, orhave been made, using a metrology apparatus such as the metrologyapparatus of FIG. 7. For example, the target can comprise a physicalinstance of the unit cell of FIG. 10A or FIG. 10B, e.g. a singleinstance or a plurality of adjacent instance as shown in FIG. 10C. In anembodiment, measurements of a plurality of targets (and thus of aplurality of physical instances of the unit cell) are obtained. In anembodiment, the measurements are of targets that are distributed acrossthe substrate. In an embodiment, a plurality of substrates, each withone or more targets (each having one or more physical instances of theunit cell), is measured. So, in an embodiment, a radiation distribution108 is obtained for each measured target.

Then, a reconstruction process at 1100, such as the reconstructionprocess described in and with respect to FIG. 9, is used to derive anominal profile of the physical instance of the unit cell, comparable tothe profile 206 of FIG. 9. The reconstruction process obtains anexpected profile 1120 of the physical instance of the unit cell to startand facilitate the reconstruction process. In an embodiment, the derivednominal profile is obtained from an average of the profile of targetsacross one or more substrates. For example, the radiation distribution108 for each target can be processed to derive a particular profile ofthat instance of the target and then the profiles for the plurality ofinstances of the target can be averaged together to derive the nominalprofile. In an embodiment, the nominal profile comprises at least ageometric profile of the target. In an embodiment, the geometric profileis a 3-D profile. In an embodiment, the nominal profile comprisesinformation regarding one or more materials properties of one or morelayers making up the physical target.

So, in an embodiment, the nominal profile can be considered as a centerof gravity for the values of various parameters of the profile of thetarget (and thus the unit cell) obtained from measuring numerousinstances of the target across the substrate and optionally on more thanone substrate. But, in an embodiment, the nominal profile can havedifferent forms and be more specific. For example, the nominal profilecan be defined for one or more particular instances of a target (e.g.,by using values from the same target location(s) from multiplesubstrates). As another example, the nominal profile can be defined fora particular substrate (e.g., by using values from only that substrate).In an embodiment, the nominal profile can be tuned for a particulartarget and/or substrate as part of the process of FIG. 12. For example,when the target and/or substrate is measured as part of the process ofFIG. 12, a reconstruction technique can be used with the measured datato fine tune the nominal profile for that target and/or substrate, thefine-tuned nominal profile can then be used as the nominal profileherein to determine weights and which weighs can then be used with thesame measured data to yield one or more overlay values.

The reconstructed nominal profile 1140 is then provided to process 1110.Thus, in an embodiment, process 1110 uses a derived nominal profile ofthe target, e.g., a geometric after-etch profile of the unit cell of adevice derived from measured data. In an embodiment, the nominal profilecan be in the form of a parameterized model, like model 206parameterized in accordance with the measured unit cell. Thus, in anembodiment, process 1110 uses a derived profile model of the unit cell,e.g., a model of the geometric after-etch profile of the physicalinstance of a unit cell of a device derived from measured data.

The basic engine of the reconstruction technique described herein isused in process 1110, along with the derived profile or the derivedprofile model, to derive the weightings. In an embodiment, the derivedprofile model or a derived profile model derived from the derivedprofile is used to determine pupil pixels sensitive to overlay in theunit cell. In particular, in an embodiment, the sensitivity to overlayof pupil response is determined by, using simulations (e.g., the Maxwellsolver), to determine a change in pupil response to an induced change inoverlay for the nominal profile.

This can be accomplished by causing the derived profile model to bechanged such that an overlay change of a certain amount is induced(e.g., 1 nm) in the model, leaving all other parameters/variables of thederived profile model unchanged. This effectively causes a symmetricunit cell to become asymmetric or causes an already asymmetric unit cellell can be symmetric) to change symmetry (including to become furtherasymmetric or to become symmetric from an asymmetric situation).

A pupil as would be expected in the metrology apparatus (e.g., forradiation at a certain measurement beam wavelength, measurement beampolarization, measurement beam intensity, etc.) can then be derived(e.g., using a Maxwell solver, a library search or other reconstructiontechnique) based on the derived profile model with the induced overlaychange. Where the physical instance of the unit cell is smaller than abeam spot, the reconstruction can treat the beam spot as being filledwith physical instances of the unit cell. In an embodiment, the derivedpupil can be a simulated pupil image 1060 and/or a derived pupil image1065 based on the simulated pupil image.

The derived pupil can be then used to determine the sensitivities of theintensity in a plurality of the pupil pixels to overlay change, forexample by comparison with a derived pupil for the unit cell without theinduced overlay (for example, the derived pupil for the unit cellwithout the induced overlay can be a simulated pupil image 1030 and/or aderived pupil image 1035 based on the simulated pupil image). In anembodiment, these sensitivities form the basis of the weightings.

In an embodiment, the pixels of the pupil (and thus the pixelintensities, signal components S_(i), etc.) can be expressed as avector. In an embodiment, the weightings can then be derived from aJacobian matrix generated in the modelling. In an embodiment, theweightings can be derived from a Moore-Penrose pseudo inverse of theJacobian matrix generated in the modelling. So, the weights areeffectively determined for the αΔx_(ov) term of equation (3). Theweightings derived from the Jacobian matrix or the Moore-Penrose pseudoinverse of the Jacobian matrix appear to apply well for the relativelymodest overlay variations (e.g., within ±3 nm or within ±4 nm or within±5 nm).

In an embodiment, the weights can be extended to be determined for theaΔx_(ov) term as well as the bΔx_(ov)Δx_(h) (and typically othercomparable terms for other parameters, such as CD, sidewall angle,etc.). In this case, the weightings are, or can be derived from, aHessian matrix generated in the modelling in addition to the Jacobianmatrix. The Hessian shows how the response to the overlay changes due toa change of a certain amount of another (symmetric) parameter (such asCD). So, for every such parameter there is a column in the Hessian. Inan embodiment, to be (more) robust, the weights could be altered suchthat they become more orthogonal to the column (parameter) for which theunit cell is sensitive. To become more orthogonal, the one or moresensitive columns can be concatenated to the Jacobian, and then theMoore-Penrose pseudo inverse can be computed from this Jacobian with oneor more columns from the Hessian concatenated thereto. From thiscomputation, the weights follow. However, this calculation can be morecomplex and thus may be suitable for those situations where overlayvalues in practice are expected to exceed the overlay variation rangefor which the weightings derived from the (Moore-Penrose pseudo inverseof) Jacobian matrix show good results.

In an embodiment, the weights can be extended to be determined for otherterms of equation (3). In that case, the weightings are, or can bederived from, third order derivatives generated in the modelling inaddition to the Jacobian matrix.

As noted above, the nominal profile could be a fine-tuned nominalprofile per target or substrate. For example, when the particular targetor substrate is measured as part of the process of FIG. 12, areconstruction technique can be used with the measured data to fine tunethe nominal profile for that target or substrate. Now, depending on thefine-tuning, the weights can be (re-)determined and/or a choice madebetween the type of weighting being made (e.g., Jacobian or acombination of the Jacobian and Hessian). For example, weights, based ona nominal profile that wasn't fine-tuned, may have been previouslyselected to suppress the effect of Δx_(h) but if the fine-tuningidentifies and updates the Δx_(h) for the target and/or substrate, theeffect of Δx_(h) may not need to be suppressed. Thus, weights could bechosen that more favor precision over robustness.

So, from process 1110, a collection (e.g., a vector) of weights w_(i)can be output. The weights w_(i) themselves can act as a conversionfactor of intensity to overlay or they can be combined with a conversionfactor from intensity to overlay (which conversion factor can be derivedas part of the same modelling). As will be appreciated from pupil image1065, the pixels in the regions 1075 and 1080 have relatively highersensitivity to overlay than pixels outside of regions 1075 and 1080 andthus their weightings will be noticeably different (e.g., higher) thanthe weighting of pixels outside of region 1075 and 1080 (which pixelshave relatively low sensitivity to overlay). So, when the weights arecombined (such as according to equation (4)) with measured intensityvalues of a target having one or more physical instances of the unitcell, an overlay signal can be obtained for the particular target (suchas a device pattern having a physical instance of the unit cell).

Further, one or more measurement parameters can be determined to form ameasurement strategy for use in obtaining the measured intensity valuesof the target. One or more measurement parameters can affect the overlaysensitivity of pixels. For example, overlay sensitivity varies acrossdifferent measurement beam wavelengths. So, in an embodiment, one ormore measurement parameters (such as wavelength, polarization, dose, anumber of optical characteristic readings taken by a detector sensor ofa particular one illumination of the target (the readings typicallyaveraged to provide an averaged optical characteristic value for themeasurement of the target)) can be varied as part of the modellingprocess 1110. For example, one or more measurement parameters can beexamined for a particular induced overlay change to determine a value ofthe one or more measurement parameters that reduces an error residual,for example between an overlay obtained when the weightings are for onevalue of the one or more parameters in relation to overlay obtained whenthe weightings are for another value of the one or more parameters, to aminimum or below a certain threshold. So, a value of one or moremeasurement parameters can then be obtained that improve precision.

Further, robustness to process variations differs across differentvalues of one or more measurement parameters. For example, inparticular, robustness to process variations differs across differentvalues of measurement beam wavelength and/or measurement polarization.Thus, in an embodiment, the weighting scheme should address at least adominant contributor to lack of robustness to process variation. So,additionally or alternatively to determining a value of one or moremeasurement parameters for improved precision, one or more measurementparameters can be examined for different particular induced overlaychange values (and/or for particular induced changes of one or moreother parameters of the derived profile model, such as a change in CD,side wall angle, etc.) to obtain a value of one or more measurementparameters that enables results using the weightings that have enhancedrobustness to process variation. For example, for different amounts ofinduced overlay change, various values of the one or more measurementparameters can be evaluated to determine a value of the one or moremeasurement parameters that causes a minimum (or below a threshold)variation in the determined overlay using the weightings associated withthe value of the one or more measurement parameters. Of course, abalance can be used in selection of the value of the one or moremeasurement parameters between precision and enhanced robustness. Forexample, a weighting can be applied between a value of the one or moremeasurement parameters determined for precision (e.g., a weight appliedto a performance metric that measures precision) and a value of the oneor more measurement parameters determined for enhanced robustness (e.g.,a weight applied to a performance metric that measures robustness) andthen a largest, top ranked, etc. combination can be selected. And ofcourse, a plurality of values of one or more measurement parameters canbe determined such that there is in effect a plurality of differentmeasurement strategies in the overall measurement strategy. Theplurality of values could be ranked according to one or more performancemetrics. Thus, optionally, a measurement strategy can be output fromprocess 1110 for use in obtaining measured intensity values of a targethaving one or more physical instances of the unit cell.

Further, one or more non-overlay parameters, such as CD, sidewall angle,etc., can affect the weights used for mapping the intensity signal tooverlay. As noted above, an example manner of determining the weights inthis context is to use a Hessian matrix and/or third order derivatives.So, in an embodiment, various possible weighting schemes are possible totake account of one or more non-overlay parameters so as to stillmaintain a good overlay value. In an embodiment, the overlay informativeoverlay pixels and their weightings can be optimized for overlaydetermination precision. This may require good model quality, i.e., goodestimates of the non-overlay parameters. In an embodiment, the overlayinformative pixels and their weights can be optimized for increasedrobustness to process variations such as in the non-overlay parameters.This may be at the expense of precision.

In an embodiment, estimates of the one or more non-overlay parameterscan be made using, for example, the reconstruction techniques describedin relation to FIG. 9, and fed-forward to tune the derived profile orderived profile model. For example, a CD reconstruction can estimate aCD of a target at a particular location at a substrate and/or for aparticular combination of patterning process settings (e.g., exposuredose, exposure focus, etc.) and use that CD estimate to tune the CDparameter of the derived profile or derived profile model. In anembodiment, iterative reconstructions of the exact derived profile orderived profile model parameters can be performed.

Referring to FIG. 12, a method of determining an overlay value for atarget having one or more physical instances of a unit cell capable ofbeing geometrically symmetric. This method involves two processes 1200and 1210. Process 1200 involves obtaining a measurement of the targethaving the one or more physical instances of the unit cell. Process 1210involves determining an overlay value for the measured target based onthe measurement of the target from process 1200.

Process 1200 takes an input the target 1220 to be measured including oneor more physical instances of a unit cell as described herein capable ofbeing geometrically symmetry. In an embodiment, a substrate with one ormore instances of the target is provided to a metrology apparatus, suchas the metrology apparatus of FIG. 7.

Optionally, process 1200 takes as input a particular measurementstrategy 1230 specified for the target. In an embodiment, themeasurement strategy can specify a value of one or more measurementparameters, such as one or more selected from: measurement beamwavelength, measurement beam polarization, measurement beam dose, and/ora number of optical characteristic readings taken by a detector sensorof the metrology apparatus of a particular one illumination of thetarget. In an embodiment, the measurement strategy can comprises aplurality of measurement strategies, each specifying a value of one ormore measurement parameters. The measurement strategy can be used tomeasure the target.

Process 1200 then measures the target using a metrology apparatusaccording to the optional measurement strategy. In an embodiment, themetrology apparatus obtains a pupil representation of the redirectedradiation. In an embodiment, the metrology apparatus can produce a pupilrepresentation such as pupil image 1030 (if, for example, the target hasno error in overlay) or pupil image 1060 (if, for example, the targethas an error in overlay). Thus, in an embodiment, the process 1200outputs optical information 1240 regarding the redirected radiation fromthe target, such as a pupil representation of the radiation.

Process 1210 then receives the optical information 1240 and processesthe optical information to determine an overlay value 1260 for thetarget. In an embodiment, the process 1210 receives as input theweightings 1250 determined from the method of FIG. 11, which then arecombined with one or more optical characteristic values (e.g.,intensities) obtained or derived from the optical information 1240.

In an embodiment, the process 1210 (or process 1200) can process theoptical information to derive a raw overlay signal from the opticalinformation. In an embodiment, the raw overlay signal comprises adifferential of the optical information, i.e., a difference in opticalcharacteristic values between symmetric pixels across an axis or pointof symmetry. In an embodiment, the derived pupil image 1035 (if, forexample, the target has no error in overlay) or derived pupil image 1065(if, for example, the target has an error in overlay) can be obtained.

In an embodiment, the weightings and optical information with respect toradiation redirected by the target (e.g., the optical information fromprocess 1200 or a processed version of the optical information fromprocess 1200 such as the raw overlay signal) are combined to determinethe overlay value. In an embodiment, the use of a combination ofredirected measurement beam intensities linearly combined withassociated weightings can lead to a quick determination of overlay. Forexample, in an embodiment, the overlay value can be derived usingequation (4) wherein the overlay value M is calculated as the weightedcombination of signal components S_(i) from the raw overlay signal usingrespective weights w_(i) for each of the signal components S_(i).

In an embodiment, the optical information collected from process 1200can be used additionally to derive one or more target related parametersother than overlay. For example, the optical information collected fromprocess 1200 can be used in a reconstruction process to derive any oneor more geometric profile parameters of the target, such as CD, sidewallangle, bottom floor tilt, etc. So, in an embodiment, a same set ofoptical information collected from a target, such as an in-dieafter-etch target, can be used to determine overlay, CD and/or one ormore other geometric profile parameters of the target (such as a devicestructure).

While, as noted above, focus has been on intensity, in an embodiment,the optical characteristic can be reflectivity, the radiation can bepolarized and the measurements can be cross-polarization measurements.For example, a target exposed to a certain linear polarization can bemeasured with that polarization or at a different polarization. So, forsymmetric pixels p_(i) and p_(i)′ (where the apostrophe denotes thesymmetric location), then reflectivity R for those pixels can bemeasured as follows:

$\begin{matrix}{{\overset{\_}{R}}_{i} = \begin{bmatrix}R_{ss} & R_{sp} \\R_{ps} & R_{pp}\end{bmatrix}} & (4) \\{{\overset{\_}{R}}_{i}^{\prime} = \begin{bmatrix}R_{ss}^{\prime} & R_{sp}^{\prime} \\R_{ps}^{\prime} & R_{pp}^{\prime}\end{bmatrix}} & (5)\end{matrix}$

wherein s denotes s polarization and p denotes p polarization. Thus, thereflectivity R_(ss) corresponds to reflectivity R of s polarizedradiation measured when the target was illuminated using s polarization,reflectivity R_(sp) corresponds to reflectivity R of s polarizedradiation measured when the target was illuminated using p polarization,and so on. Moreover, these measurements can be taken at differentwavelengths. And, it has been discovered that, in certain embodiments,the overlay for a symmetric unit cell that changes its symmetry inresponse to overlay change can be found and determined from thecongruents R_(ps) and R_(sp).

Further, non-linearity can arise from overlay and/or from otherparameters. As discussed above, certain non-linearity can be addressedthrough appropriate selection of weightings, e.g., by deriving theweightings using a Hessian matrix and/or third order derivatives. In anembodiment, the non-linearity can be addressed by using a non-linearsolution to derive the overlay from the measured optical information ofredirected radiation from a target.

In an embodiment, the overlay can be determined through using thereconstruction engine as described above used to derive the nominalprofile. For example, a non-linear solver working from a model based onthe derived nominal profile and/or a derived nominal profile model canbe used to derive a simulated version of the optical informationexpected from redirected radiation from a target of interest, which canbe compared to the measured optical information of the target ofinterest. As noted above, the target of interest comprises one or morephysical instances of a unit cell that can be symmetric and that changesits symmetry when subject to overlay. Then, if there is not agreementwithin a certain threshold, a geometric profile parameter (e.g.,overlay) can be varied and the simulated version of the opticalinformation re-computed and compared to the measured optical informationuntil there is agreement within a threshold. Similarly, measured opticalinformation of a target of interest can be compared against a library ofthe optical information expected from redirected radiation from thetarget of interest (which library would typically be derived using anon-linear solver). Then, if there is not agreement within a certainthreshold, a geometric profile parameter (e.g., overlay) can be variedand the library can be consulted again for a simulated version of theoptical information which is compared to the measured opticalinformation until there is agreement within a threshold.

In an embodiment, the use of the reconstruction engine with the measuredoptical information from a target of interest uses measured opticalinformation from which a symmetric distribution of radiation has beenremoved as described above, e.g., by subtracting from the opticalcharacteristic value at each pixel the optical characteristic value at apixel symmetrically located across a point or axis of symmetry. Thus,the optical information relates to substantially only the asymmetricdistribution of radiation. Similarly, the simulated or library versionof the optical information relates to substantially only the asymmetricdistribution of radiation. This will facilitate the speed of calculationand/or comparison as a significant portion of optical information won'tneed to be calculated or evaluated since it will eliminate through thedifferencing.

In a further embodiment of a non-linear solution, the expansion ofequation (3) can be solved with a non-linear solver to derive Δx_(ov).In particular, the values of (a−a′), (b−b′), (c−c′), etc. (asapplicable) in equation (3) can be determined as part of thedetermination of the derived nominal profile and/or the derived nominalprofile model of a unit cell of interest. For example, once the derivednominal profile has been determined as part of the non-linearreconstruction, simulated or library optical information for a pupilcorresponding to the derived nominal profile (e.g., corresponding to aperturbation of the derived nominal profile for a particular change inoverlay (e.g., Δx_(ov))) can be obtained and then the values of a, b, c,etc. (as applicable) can be determined for each pixel in the pupil witha non-linear solver that, e.g., iterates through solutions (e.g.,responsive to one or more perturbations in overlay (e.g., Δx_(ov))) inorder to minimize the residual. The result is a vector of a values forthe pupil (each a value corresponding to a pixel of the pupil), a vectorof b values for the pupil (each b value corresponding to a pixel of thepupil), a vector of c values for the pupil (each a value correspondingto a pixel of the pupil), and so on as applicable. These vectors canthen be combined with a vector of S_(i) values determined from ameasured pupil of a target having the unit cell of interest. Anon-linear solver that, e.g., iterates through solutions in order tominimize the residual, can take these input vectors and then solve forthe overlay Δx_(ov).

While the discussion above has focused on using a model that models thephysical profile of the unit cell, in an embodiment, the weightings canbe derived using a data driven technique that does not require physicalprofile modelling or can be derived with a data driven technique thatsupplements physical profile modeling. So, in an embodiment, the datadriven technique can advantageously not require a physical profilemodel; this can be useful, for example, for limiting the sharing ofconfidential information because the physical profile modeling startswith, and determines, details regarding the unit cell (and thus thetarget) which can be sensitive information if the unit cell is a devicepattern structure. In an embodiment, the data driven technique can beenable relatively quick determination of, for example, the weights asdiscussed above to translate measured optical information (e.g., pupilintensity) into a patterning process parameter (e.g., overlay). In anembodiment, the data driven technique enables determination of thepatterning process parameter in an early stage since as discussed belowthe data technique driven may need only measured data and an associatedreference.

So, in an embodiment, the data driven technique involves processing datameasured (“get” data) from one or more substrates having physicalinstances of the unit cell of interest patterned thereon as one or moretargets, with one or more certain set values of the patterning processparameter (e.g., overlay) of interest. This combination of “set”intentional values of a certain patterning process parameter (e.g.,overlay) to create patterns along with data measured from those patterns(“get” data) is referred to as a “set-get” process. For example, anoverlay of a particular amount of the physical instance of unit cell iscreated as part of the patterning process and then the target having thephysical instance of the unit cell is measured to obtain, e.g., a pupilimage thereof (i.e., “get” data). In an embodiment, a plurality ofsubstrates can be patterned and measured in this manner. In anembodiment, a plurality of different set values of overlay are created,which different values of overlay can be on one substrate, can be acrossdifferent substrates, etc. In an embodiment, each substrate will have aplurality of targets measured, yielding, e.g., a plurality of pupilimages. In an embodiment, the overlay can be created by inducing amagnification change from the design magnification between patterningdifferent parts of the physical instance of the unit cell. In anembodiment, the overlay can be created by providing an intentionaltranslation from the design positioning between patterning differentparts of the physical instance of the unit cell. Thus, the result is adeliberate applied overlay in targets that are, e.g., induced by thelithographic apparatus.

In an embodiment, in general, there is obtained measurement data andassociated reference values. So, in an embodiment, deliberate overlayneed not be provided if there are different overlays but those overlaysare determined by another means (e.g., from a scanning electronmicroscope). In an embodiment, critical dimension uniformity substrateswith corresponding reference data (e.g. coming from a CD-SEM) can beused as the input data. With the measured data and the reference values,the data-driven approach can find, as discussed herein, weights suchthat inferred overlay values resemble the reference values. So, whilethe discussion of the data-driven technique will focus on measuredoptical information and pupil representations obtained at intentionallyset overlay value, they can be generally applied to more generalmeasurement data and associated reference values (whether measured orintentionally set).

Further, while the techniques here relate to a particular overlay (e.g.,an overlay in the X-direction), it will be appreciated that thetechniques here can be repeated for different overlays (e.g., an overlayin the Y-direction, overlay between structures in different layers,etc.) using corresponding measurement data and reference values. Thus,different weights sets can be determined for different overlays.

So, referring to FIG. 13, a high-level flow of an embodiment of a datadriven technique is depicted. At 1300, a calculation is performed toderive the weights as discussed above to translate measured opticalinformation (e.g., pupil intensity) into a patterning process parameter(e.g., overlay). In particular, the calculation uses several inputs. Oneof the inputs is the set values 1320 of a set-get process for a targethaving a physical instance of the unit cell of interest. As noted above,a plurality of instances of a target can be measured across one or moresubstrates, wherein one or more instances of the target have a differentvalue of intentional set value of a patterning process parameter thanone or more other instances of the target. A further input is measuredoptical information 1310 for those instances of the target at differentset values. In an embodiment, the optical information 1310 is aplurality of pupil representations, each corresponding to an instance ofthe target. Then, inputs 1310 and 1320 are processed in a data driventechnique to arrive at the weights 1330. Examples of such a data driventechnique are described hereafter.

In an embodiment, an example of a data driven technique to find a vectorof the weights w is to minimize the following objective or meritfunction to arrive at the weights w:

$\begin{matrix}{\underset{\underset{\_}{w},\underset{\_}{c}}{\arg \; \min}{\sum_{i = 1}^{D}{{{P_{i}^{T}\underset{\_}{w}} - \underset{\_}{s_{i}} - {\underset{\_}{1}\; c_{i}}}}^{2}}} & (6)\end{matrix}$

wherein w is a vector of the weights for combination with values of ameasured optical characteristic (e.g., intensity) to determine apatterning process parameter (e.g., overlay), each weight correspondingto a pixel value of the pupil, P_(i) is a matrix with each columncontaining the pixel values of the measured optical characteristic froma measured pupil of an instance of a target obtained from a substrate ipatterned so as to obtain a particular set value of the patterningprocess parameter (which matrix is then transposed so that the columnsbecomes the pixels of the pupil, the rows become the one or moreinstances of the target on the substrate, and the values in the matrixare the values of measured optical characteristic at the respectivepixels), s_(i) is a vector containing the corresponding set values ofthe patterning process parameter for the one or more instances of thetarget on the one or more substrates i, each set value corresponding toa patterning process parameter value, 1 is a unit vector of the size ofthe number of set values, and c_(i) is an offset difference between theset-values of the patterning process parameter and inferred values ofthe patterning process parameter (P_(i) ^(T) w) for each substrate, andD is the number of substrates measured. The matrix P_(i) can becombination of different results for each instance of the target. Forexample, a target can be measured with different wavelengths, differentpolarizations, etc. So, these results can be concatenated to each columnso, for example, a single column can have values for the pixels of apupil a target measured with a first wavelength and a firstpolarization, which are followed by values in the column for pixels of apupil of the target measured with a second different wavelength orfollowed by values in the column for pixels of a pupil of the targetmeasured with a second different polarization (and which can then befollowed by further values at one or more different polarizations and/orwavelengths).

So, in effect, this function finds the weight vector w, such that theinferred values P_(i) ^(T) w for each substrate i looks as similar aspossible (in a L2 regularization norm sense) as the set-values s_(i)apart from an offset c_(i). In principle, the optimal weights andoffsets can be computed by a matrix inversion. Since the pixel values ofthe measured optical characteristic are taken with one or moreparticular metrology apparatuses, the obtained weights can be normalizedby calibration data to reduce the impact of the particular metrologyapparatus itself on the results.

Instead of or in addition to finding the weights as described aboveusing an objective or merit function as the data driven technique, thedata driven technique can use a machine learning algorithm, like aneural network, or a non-linear method to determine the weights based onmeasured pupils of targets with intentionally provided difference in thepatterning process parameter (e.g., overlay) of interest.

In an embodiment, after the training (i.e., using the objective or meritfunction or the machine learning algorithm), the weights can checkedusing other data. There is a chance that the training results in anoverfit; the data driven approach “just” fits the data to the setvalues. Therefore, a cross validation is done. New data with known setvalues are used to check the weights. This new data can also be a subsetof the substrates at hand. So, in an embodiment, the training is done ona subset of substrates, and the validation is done on another (disjunct)subset of substrates.

FIG. 14 depicts a high-level flow of an embodiment of a data driventechnique in combination with a physical geometric model. In thisembodiment, a data driven technique as described in relation to FIG. 13can be used to derive weights, which are used to tune a physicalgeometric model (e.g., by using the Hessian to obtain better modelnominal values, by changing the model nominal values, etc.) such thatweights from physical geometric model (e.g., the (Moore-Penrose pseudoinverse of the) Jacobian of the physical geometric model) are the sameor similar (e.g., in value, statistically, etc.) to the weightsdetermined by the data driven technique. Thus, in an embodiment, a(scaled) weight vector w can be used to fine-tune the physical geometricmodel such that the physical geometric model is tuned so that the(Moore-Penrose pseudo inverse of) the Jacobian is similar to the(scaled) weight vector w.

So, in an embodiment, at 1400, a data driven technique (examples ofwhich are described above) is performed to derive the weights asdiscussed above. The calculation uses several inputs. One of the inputsis the set values 1420 of a set-get process for a target having aphysical instance of the unit cell of interest. As noted above, aplurality of instances of a target can be measured across one or moresubstrates, wherein one or more instances of the target have a differentvalue of intentional set value of a patterning process parameter thanone or more other instances of the target. A further input is measuredoptical information 1410 for those instances of the target at differentset values. In an embodiment, the optical information 1410 is aplurality of pupil representations, each corresponding to an instance ofthe target. Then, inputs 1410 and 1420 are processed in a data driventechnique to arrive at the weights 1430.

The weights 1430 are input to a process 1440 to fine-tune a physicalgeometric model using the weights 1430. The process 1440 obtains aphysical profile 1450 for the unit cell (which the process 1440 uses toderive a physical profile model) or obtains a physical profile model1450 for the unit cell (which the process 1440 uses). In an embodiment,the physical profile is the derived nominal profile and/or the derivednominal profile model of a unit cell as discussed above.

The process 1440 uses the physical geometric model to derive weightsthat correspond to weights 1430. Those weights are then compared to theweights 1430. The comparison can involve a matching of magnitudes, astatistical analysis, a fitting evaluation, etc. If there is asignificant difference (e.g., by evaluation of the comparison against athreshold), one or more parameters of the physical profile can be tuned.For example, one or more physical profile parameters (e.g., CD, sidewallangle, material heights, etc.) can be tuned so that the results of thecomparison come closer than or equal to, e.g., a certain threshold. Inan embodiment, the Hessian can be used to do this fine-tuning, or can bedone using a non-linear solver (including one or more forward calls(e.g., a Maxwell solver)). The tuning and comparison can be iterateduntil the threshold is met or crossed. Then, the tuned physicalgeometric model can output updated weights 1460 for use in combiningwith measured optical information of a target of interest to derive apatterning process parameter value.

FIG. 15 depicts a high-level flow of a further embodiment of a datadriven technique in combination with a physical geometric model. When aphysical geometric model behaves similarly as measured data, thephysical geometric model can be used to predict the impact of processvariations. So, in an embodiment, the Hessian of the physical geometricmodel can be used to tune the weights such that the weights become(more) orthogonal to process variations that were not in the data usedin the data driven technique to obtain the weights used to tune thephysical geometric model.

This approach of using the Hessian to tune the weights can also be donewithout the data driven technique. That is, this technique to use theHessian to update the weights can be done with a physical geometricmodel approach described in association with FIG. 11. In this case, forexample, the weights can be tuned such that the weights become (more)orthogonal to process variations that were not in the data used toobtain the derived nominal profile and/or the derived nominal profilemodel of a unit cell as discussed above. Through such tuning, theweights become more robust to process variations not observed inmeasured data used to create the physical geometric model.

So, in an embodiment, at 1500, a data driven technique (examples ofwhich are described above) is performed to derive the weights asdiscussed above. The calculation uses several inputs. One of the inputsis the set values 1510 of a set-get process for a target having aphysical instance of the unit cell of interest. As noted above, aplurality of instances of a target can be measured across one or moresubstrates, wherein one or more instances of the target have a differentvalue of intentional set value of a patterning process parameter thanone or more other instances of the target. A further input is measuredoptical information 1505 for those instances of the target at differentset values. In an embodiment, the optical information 1505 is aplurality of pupil representations, each corresponding to an instance ofthe target. Then, inputs 1505 and 1510 are processed in a data driventechnique to arrive at the weights 1515.

The weights 1515 are input to a process 1520 to fine-tune a physicalgeometric model using the weights 1515. The process 1520 obtains aphysical profile 1525 for the unit cell (which the process 1520 uses toderive a physical profile model) or obtains a physical profile model1525 for the unit cell (which the process 1520 uses). In an embodiment,the physical profile is the derived nominal profile and/or the derivednominal profile model of a unit cell as discussed above.

The process 1520 uses the physical geometric model to derive weightsthat correspond to weights 1515. Those weights are then compared to theweights 1515. The comparison can involve a matching of magnitudes, astatistical analysis, a fitting evaluation, etc. If there is asignificant difference (e.g., by evaluation of the comparison against athreshold), one or more parameters of the physical profile can be tuned.For example, one or more physical profile parameters (e.g., CD, sidewallangle, material heights, etc.) can be tuned so that the results of thecomparison come closer than or equal to, e.g., a certain threshold. Inan embodiment, the Hessian can be used to do this fine-tuning, or can bedone using a non-linear solver (including one or more forward calls(e.g., a Maxwell solver)). The tuning and comparison can be iterateduntil the threshold is met or crossed.

But, as will be appreciated, a patterning process can vary duringexecution and differently for different executions of the patterningprocess. Thus, data obtained for the data driven technique doesn'taccount for all the possible patterning process variations. But, whenthe tuning of the physical geometric model has made it so that behavessimilarly as measured data, the physical geometric model can be used topredict the impact of process variations and adjust the weightsaccordingly.

So, in an embodiment, the tuned physical geometric model 1530 is used tocompute the Hessian of the tuned physical geometric model at 1535. TheHessian 1540 is then used to tune the weights at 1545 such that theweights become (more) orthogonal (i.e., robust) to process variationsthat were not in the data used in the data driven technique to obtainthe weights used to tune the physical geometric model. In other words,the weights are tuned to be more likely to yield an accurate result whencombined with measurement data from a substrate even when the substrateis subject to process variation.

A non-limiting example of how the Hessian can be used to fine-tune theweights is described here in the context of overlay; a differentpatterning process parameter could be used as appropriate. In thisexample, it is assumed only one overlay type is evaluated (e.g., overlayin the X direction). Fine-tuning with multiple overlay types is alsopossible.

In this embodiment of using the Hessian to fine-tune the weights, anoverlay response is estimated from data measured from one or moreset-get substrates by applying a single value decomposition to the data.It is assumed that an eigenvector d(which has length 1) corresponds tothe overlay response. Then the following equation is solved to findvector Δp:

$\begin{matrix}{\underset{\underset{\_}{\Delta \; p}}{\arg \; \min}{{\underset{\_}{d} - \frac{\underset{\_}{J} + {H\; \underset{\_}{\Delta \; p}}}{{\underset{\_}{J} + {H\; \underset{\_}{\Delta \; p}}}}}}} & (7)\end{matrix}$

wherein J is the Jacobian with respect to the overlay parameter, and theHessian H is a matrix where the columns contain the partial derivativeswith respect to a process variation (e.g., a variation in CD, materialheight, etc.) and the overlay parameter (both the Jacobian and theHessian are obtained from the model as described above). The determinedvector Δp then corresponds to the delta parameters to be applied to thenon-overlay parameters in the model to obtain an updated (e.g., better)model.

To make the weights robust to process variations (i.e. orthogonal to theprocess variations), the following technique can be used. A pupil/can bedefined by the following second order Taylor expansion:

I=Jo+H Δp o  (8)

where J is the Jacobian with respect to the overlay parameter, and H isa matrix where the columns contain the partial derivatives with respectto a process variation (e.g., a variation in CD, material height, etc.)and the overlay parameter. The vector Δp contains the correspondingprocess variations. Thus, for a given structure and for a given processvariation instance Δp with an overlay value o, the pupil equals(approximately) I. As will be appreciated, the above formulation can beextended to more overlay parameters by adding these contributions aswell. Moreover, this formulation is an approximation because the higherorders in the Taylor expansion are neglected.

Now, if the impact of the process variations is small, the weights arecomputed using the Penrose-Moore inverse of the Jacobian J. In the caseof only one overlay parameter, the weights equal to

$\underset{\_}{w} = {\frac{\underset{\_}{J}}{{\underset{\_}{J}}^{2}}.}$

And indeed, the weighted average (inner product) with the pupil resultsin the overlay value o (Δp=0), i.e.,

$\begin{matrix}{{\langle{\underset{\_}{I},\underset{\_}{w}}\rangle} = {{\langle{{\underset{\_}{J}o},\underset{\_}{w}}\rangle} = {{\frac{o}{{\underset{\_}{J}}^{2}}{\langle{\underset{\_}{J},\underset{\_}{J}}\rangle}} = o}}} & (9)\end{matrix}$

However, when the process variations have a large impact, the overlayresponse changes:

I =( J+H Δp )o= {tilde over (J)} o  (10)

To make the weights robust to these variations,

Hw =0  (11)

This can be achieved by taking the weights w equal to the first row ofthe pseudo inverse of the matrix [J H]. Or in other words, the Hessianmatrix H is concatenated to the Jacobian before the inversion. In thisway, the weights become orthogonal to the process variations (but atsome cost of precision).

Thus, from tuning 1545, tuned weights 1550 are output for use incombining with measured optical information of a target of interest toderive a patterning process parameter value.

FIG. 16 depicts a high-level flow of a further embodiment of a datadriven technique in combination with a physical geometric model. In thisembodiment, the data input to the data driven technique is extended byincluding synthetic optical information (e.g., pupil representations)that contains process variations for the patterning process (e.g. thepatterning process variation can be obtained from CD measurements). Thesynthetic optical information alone or in combination with the measuredoptical information can be used to find new weights using the datadriven technique.

So, in an embodiment, at 1500, a data driven technique (examples ofwhich are described above) is performed to derive the weights asdiscussed above. The calculation uses several inputs. One of the inputsis the set values 1510 of a set-get process for a target having aphysical instance of the unit cell of interest. As noted above, aplurality of instances of a target can be measured across one or moresubstrates, wherein one or more instances of the target have a differentvalue of intentional set value of a patterning process parameter thanone or more other instances of the target. A further input is measuredoptical information 1505 for those instances of the target at differentset values. In an embodiment, the optical information 1505 is aplurality of pupil representations, each corresponding to an instance ofthe target. Then, inputs 1505 and 1510 are processed in a data driventechnique to arrive at the weights 1515.

The weights 1515 are input to a process 1520 to fine-tune a physicalgeometric model using the weights 1515. The process 1520 obtains aphysical profile 1525 for the unit cell (which the process 1520 uses toderive a physical profile model) or a physical profile model 1525 forthe unit cell (which the process 1520 uses). In an embodiment, thephysical profile is the derived nominal profile and/or the derivednominal profile model of a unit cell as discussed above.

The process 1520 uses the physical geometric model to derive weightsthat correspond to weights 1515. Those weights are then compared to theweights 1515. The comparison can involve a matching of magnitudes, astatistical analysis, a fitting evaluation, etc. If there is asignificant difference (e.g., by evaluation of the comparison against athreshold), one or more parameters of the physical profile can be tuned.For example, one or more physical profile parameters (e.g., CD, sidewallangle, material heights, etc.) can be tuned so that the results of thecomparison come closer than or equal to, e.g., a certain threshold. Thetuning and comparison can be iterated until the threshold is met orcrossed.

So, in an embodiment, the tuned physical geometric model 1530 is used tocompute the Hessian of the tuned physical geometric model at 1535. TheHessian 1600 is then used to generate at 1610 synthetic opticalinformation (e.g., one or more pupil representations). Synthetic opticalinformation is simulated optical information. The synthetic opticalinformation is intended to mimic one or more expected process variationsin the patterning process. In an embodiment, data 1620 regarding one ormore process variations in the patterning process can be used incombination with the Hessian 1600 to derive the synthetic opticalinformation. In an embodiment, a synthetic pupil I can be generated bysubstituting different overlay values o and different parametervariations Δp in the equation (8) above, wherein the weights correspondto

$\underset{\_}{w} = {\frac{\underset{\_}{J}}{{\underset{\_}{J}}^{2}}.}$

While equation (8) described above is directed to a single overlayparameter, the technique can be extended to more overlay parameters byadding those contributions as well. Furthermore, the technique usingequation (8) is an approximation, because the higher orders in theTaylor expansion are neglected. The data 1620 can comprise, for example,information that describes the kind and extent of a process variation(e.g., an indication that overlay, CD, etc. can vary by a certainpercentage). The data 1620 can be obtained by a measurement in thepatterning process, e.g., overlay, CD, etc. measurement. The data 1620is thus used with the Hessian 1600 to generate simulated opticalinformation 1630 that includes an expected process variation. Thesynthetic optical information 1630 can also include one or moreassociated estimated set values associated with the synthetic opticalinformation 1630. The synthetic optical information 1630 (and anyassociated set values) is then input to the data driven technique 1500for analysis alone or in combination with the measured opticalinformation, to find new weights using the data driven technique.

FIG. 17 depicts a high-level flow of a further embodiment of a datadriven technique in combination with a physical geometric model. Thisembodiment is similar to the embodiment of FIG. 16 except that insteadof computing a Hessian a forward call is made to a non-linear solver(e.g., a Maxwell solver) for every process variation to obtain thesynthetic optical information.

So, in an embodiment, at 1500, a data driven technique (examples ofwhich are described above) is performed to derive the weights asdiscussed above. The calculation uses several inputs. One of the inputsis the set values 1510 of a set-get process for a target having aphysical instance of the unit cell of interest. As noted above, aplurality of instances of a target can be measured across one or moresubstrates, wherein one or more instances of the target have a differentvalue of intentional set value of a patterning process parameter thanone or more other instances of the target. A further input is measuredoptical information 1505 for those instances of the target at differentset values. In an embodiment, the optical information 1505 is aplurality of pupil representations, each corresponding to an instance ofthe target. Then, inputs 1505 and 1510 are processed in a data driventechnique to arrive at the weights 1515.

The weights 1515 are input to a process 1520 to fine-tune a physicalgeometric model using the weights 1515. The process 1520 obtains aphysical profile 1525 for the unit cell (which the process 1520 uses toderive a physical profile model) or a physical profile model 1525 forthe unit cell (which the process 1520 uses). In an embodiment, thephysical profile is the derived nominal profile and/or the derivednominal profile model of a unit cell as discussed above.

The process 1520 uses the physical geometric model to derive weightsthat correspond to weights 1515. Those weights are then compared to theweights 1515. The comparison can involve a matching of magnitudes, astatistical analysis, a fitting evaluation, etc. If there is asignificant difference (e.g., by evaluation of the comparison against athreshold), one or more parameters of the physical profile can be tuned.For example, one or more physical profile parameters (e.g., overlay, CD,sidewall angle, etc.) can be tuned so that the results of the comparisoncome closer than or equal to, e.g., a certain threshold. The tuning andcomparison can be iterated until the threshold is met or crossed.

So, in an embodiment, the tuned physical geometric model 1700 is used tocompute at 1720 synthetic optical information like as discussed above.Like as discussed above, data 1710 regarding one or more processvariations in the patterning process can be used in combination with thetuned physical geometric model 1700 to derive the synthetic opticalinformation. For example, the data 1710 can comprise information thatdescribes the kind and extent of a process variation (e.g., anindication that overlay, CD, etc. can vary by a certain percentage). Thedata 1710 can be obtained by a measurement in the patterning process,e.g., overlay, CD, etc. measurement. As noted above, the process at 1720can use a forward call to a non-linear solver (e.g., a Maxwell solver)for the process variation to obtain the synthetic optical information.The data 1710 is thus used with the tuned physical geometric model 1700to generate simulated optical information 1730 that includes an expectedprocess variation. The synthetic optical information 1730 can alsoinclude one or more associated estimated set values associated with thesynthetic optical information 1730. The synthetic optical information1730 (and any associated set values) is then input to the data driventechnique 1500 for analysis alone or in combination with the measuredoptical information, to find new weights using the data driventechnique.

In FIGS. 10A-10C, a relatively simple example of a unit cell waspresented in which an overlay in essentially only one direction caused achange in the symmetry of the unit cell. In particular, in the unit cellof FIGS. 10A-10C, an overlay change in the X direction resulted in achange in the symmetry/asymmetry of the unit cell, while an overlaychange in the Y direction does not result in a change in the symmetry ofthe unit cell. This is a consequence of the unit cell of FIGS. 10A-10Chaving two structures 1000, 1005 which are configured in a particulargeometric way such that an overlay in essentially only one directioncaused a change in the symmetry of the unit cell. Of course, this can bedesigned in this manner by appropriate selection of structures. However,it could be that an existing structure, such as a device structure, canbe identified that has a particular geometry such that an overlay inessentially only one direction causes a change in the symmetry of theunit cell. So, various unit cells can be chosen or designed that enabledetermination of an overlay in essentially only one direction (whichneed not be in the X direction).

However, advantageously, a unit cell can be identified or designed thatis configured so that a change in the symmetry of the unit cell resultsfor two or more different overlays. In an embodiment, the differentoverlays can be in different directions. Specifically, in an embodiment,a first overlay can be in the X direction, while a second overlay can bein the Y direction. In an embodiment, the different overlays can each bebetween a different combination of structures or parts of the unit cell.In an embodiment, those structures can be in a same layer and/or indifferent layers of the target. Specifically, in an embodiment, a firstoverlay can be between a first structure and a second structure of theunit cell and a second overlay can be between the first structure (orsecond structure) and a third structure of the unit cell or between athird structure and a fourth structure of the unit cell. In this case,the first overlay and second overlay can be in the same direction.Naturally, there can be a combination of different overlays in differentdirections and different overlays from combinations of structures of theunit cell. For example, a first overlay can be in the X direction for afirst structure in a first layer and a second structure in a secondlower layer and a second overlay can be in the Y direction for the firststructure in the first layer and a third structure in the a third layerlower than the second layer. Thus, numerous combinations of overlay canbe determined through appropriate identification or design of the unitcell (and thus the target).

Moreover, as will be appreciated, a determination of an overlay in the Xdirection and the Y direction can enable through appropriate combinationdetermine a total overlay (in X and Y). Similarly, to enable thedetermination of total overlay for multiple different structures betweenwhich overlay can occur, the overlay for each of those structures needsto be determined. So, as an example, for a unit cell that has 4 distinctstructures in 4 layers between which overlay can occur (with one of thelayers being a reference layer), then 6 overlays (X and Y for eachlayer) could be determined to enable determination of the total overlayfor the unit cell. Of course, a sub-combination could be determined asdesired to arrive at one or more different overlays of interest amongthe 4 layers.

FIG. 18 depicts an example embodiment of a multiple overlay unit cell ofa target. Like the unit cells of FIGS. 10A-10C, this unit cell comprisesa first structure 1000 and a second structure 1005. Additionally, thisunit cell has a third structure 1800 that is in this embodiment in alayer above, in the Z direction, the first and second structures 1000,1005. In this embodiment, asymmetry of this unit cell can be created byone or more different overlays.

For example, a relative shift between the structure 1005 and thestructure 1800 in the X direction can yield an overlay in the Xdirection which causes asymmetry. As another example, a relative shiftbetween the structure 1005 and the structure 1000 in the Y direction canyield an overlay in the Y direction which causes asymmetry. As a furtherexample, a relative shift between the structure 1000 and the structure1800 in the Y direction can yield a further overlay in the Y directionwhich causes asymmetry.

FIG. 19 depicts a further example embodiment of a multiple overlay unitcell of a target. Like the unit cells of FIGS. 10A-10C, this unit cellcomprises a first structure 1000 and a second structure 1005.Additionally, like the unit cell of FIG. 18, this unit cell has a thirdstructure 1800 that is in this embodiment in a layer above, in the Zdirection, the first and second structures 1000, 1005. Further, thisunit cell has a fourth structure 1900 that is in this embodiment in alayer above, in the Z direction, the first, second and third structures1000, 1005, 1800. Like the unit cell of FIG. 18, in this embodiment,asymmetry of this unit cell can be created by one or more differentoverlays. For example, a relative shift between the structure 1005 andthe structure 1800 in the X direction can yield an overlay in the Xdirection which causes asymmetry. As another example, a relative shiftbetween the structure 1005 and the structure 1900 in the X direction canyield an overlay in the X direction which causes asymmetry. As anotherexample, a relative shift between the structure 1005 and the structure1000 in the Y direction can yield an overlay in the Y direction whichcauses asymmetry. As a further example, a relative shift between thestructure 1000 and the structure 1800 in the Y direction can yield afurther overlay in the Y direction which causes asymmetry.

Thus, in an embodiment, measurement of an illuminated physical instanceof the unit cell of FIG. 18 or of FIG. 19 will yield optical informationthat could potentially include multiple different overlays if there arein fact multiple different overlays. For example, referring to FIG. 18,if the symmetry of the unit cell of FIG. 18 represents zero overlay andthere is a shift in the X and Y of the structure 1005 (e.g., a shift indirection that is not 0, 90, 180 or 270 degrees) from its zero overlayposition relative to its overlying structures, that shift would cause anasymmetry due to the relative shift between the structure 1005 and thestructure 1800 in the X direction and the relative shift between thestructure 1005 and the structure 1000 in the Y direction. So, it wouldbe desirable to determine both the overlay for structure 1005 in the Xand Y directions (which combination will yield the total overlay ofstructure 1005).

As discussed hereafter, a technique is presented that can determine,from the optical characteristic values, a value of a first overlay forthe physical instance of the unit cell separately from a second overlayfor the physical instance of the unit cell that is also obtainable fromthe same optical characteristic values, wherein the first overlay is ina different direction than the second overlay (e.g., X direction overlayand Y direction overlay) or between a different combination of parts ofthe unit cell than the second overlay (e.g., a first overlay betweenstructure 1005 and structure 1800 and a second overlay between structure1005 and structure 1000 or between structure 1000 and structure 1800,where the first overlay and the second overlay could possibly be in thesame direction).

That is, in an embodiment, weights are determined to decouple firstoverlay information in an optical characteristic value from second (ormore) overlay information in the same optical characteristic value.Thus, in an embodiment, by applying specially selected weights, thecombination of the weights with optical characteristic values will yielda particular overlay of interest as distinguished from other possibleoverlay information in the same optical characteristic values. Ineffect, the weights will feature the overlay of interest and lessen oneor more other overlays. Of course, different sets of weights can beconstructed for each overlay of interest such that the opticalcharacteristic values can be processed to yield different values foreach of the different overlays of interest.

This technique will be described in respect of the graph of FIG. 20. Thegraph of FIG. 20 presents a graphical presentation of the technique butin practice the graph need not be constructed as all the processing canbe done mathematically without the need to create the graph. Further,the technique is described in respect of the model of FIG. 11. But,models (and associated other techniques) described in respect of otherFigures herein could be used.

Further, this example is presented in terms of deriving the linearversion of the weights from the model. That is, in an embodiment, theweights are derived from the (Moore-Penrose pseudo inverse of) theJacobian.

So, in this linear case, to reconstruct a particular parameter such asan overlay in a certain direction, the Jacobian can be inverted. But,how the column of the parameter of interest is correlated to theremaining columns determines how easily it will be to reconstruct thisparameter.

So, having, e.g., the nominal profile model for a unit cell of interest(e.g., the unit cell of FIG. 18), at least two vectors can be generated.A first overlay vector p₁ represents a first overlay of interest (e.g.,a X-direction overlay) within the unit cell and a second overlay vectorp₂ represents a second overlay of interest (e.g., a Y-directionoverlay). As will be appreciated, further vectors can be created foradditional overlays of interest.

Further, for each of the two overlay vectors, one or more pixels of apupil representation corresponding to an expected measurement of thephysical instance of the unit cell are selected. In this embodiment, apair of pixels is selected for each overlay vector, wherein each pair ofpixels comprises symmetrically located pixels as described earlier.Desirably, the pairs of pixels are selected from the asymmetricradiation distribution portion of the pupil representation as discussedabove.

Now, the first overlay vector p₁ corresponds to the response (in thiscase, asymmetric signal between the pixels creating a pair) in the pairsof pixels to a change in the first overlay of interest for the firstoverlay vector (leaving all other parameters unchanged, i.e., no changein the second overlay of interest). This response can be generated usingthe nominal profile model by inducing a change in the first overlay ofinterest (e.g., 1 nm change) and then calculating the optical response(e.g., intensity) in the pairs of pixels to that change.

Similarly, the second overlay vector p₂ corresponds to the response (inthis case, asymmetric signal between the pixels creating a pair) in thepairs of pixels to a change in the second overlay of interest for thesecond overlay vector (leaving all other parameters unchanged, i.e., nochange in the first overlay of interest). This response can be generatedusing the nominal profile model by inducing a change in the secondoverlay of interest (e.g., 1 nm change) and then calculating the opticalresponse (e.g., intensity) in the pairs of pixels.

The resulting vectors are graphed in FIG. 20 wherein the horizontal axisu corresponds to the asymmetric intensity (I_(i)−I_(i)′) betweensymmetrically positioned pixels of the first pixel pair and the verticalaxis v corresponds to the asymmetric intensity (I_(i)−I_(i)′) betweensymmetrically positioned pixels of the second pixel pair. So, FIG. 20shows two highly correlating vectors p₁ and p₂ .

So, to decouple and separate the contributions of the first and secondoverlays of interest to the pixel pairs, the vector p₁ is back-projectedonto a vector P₂ ^(⊥) , which is a vector orthogonal to the vector p₂ ,to form vector p₁′ and the length of projected vector p₁′ is divided bythe cosine of the angle θ₁ between vector p₁ and P₂ ^(⊥) . This vectorthen helps to isolate the first overlay of interest from the intensityof the pixel pairs (and by extension other pixel pairs in the pupilrepresentation).

Additionally or alternatively, the vector p₂ is back-projected onto avector P₁ ^(⊥) , which is a vector orthogonal to the vector p₁ , to formvector p′₂ and the length of projected vector p′₂ is divided by thecosine of the angle θ₂ between vector p₂ and P₁ ^(⊥) . This vector thenhelps to isolate the second overlay of interest from the intensity ofthe pixels pairs (and by extension other pixel pairs in the pupilrepresentation).

So, referring back to equations (3) and (4), S_(i) represents theasymmetric intensity (I_(i)−I_(i)′) between symmetrically positionedpixels of a pixel pair. So, the first overlay vector p₁ can correspondto the response in a first pixel pair having S_(i) of U₀ and a secondpixel pair having S_(i) of V₀ to a change in the first overlay ofinterest. Similarly, the second overlay vector p₂ can correspond to theresponse in those first and second pixel pairs to a change in the secondoverlay of interest. Accordingly, the vector p₁′ and/or the vector p₂′can be constructed; here both are constructed for explanatory purposes.The vector p₁′ and the vector p₂′ are defined in terms of the intensityu corresponding to the first pixel pair corresponding to U₀ and in termsof the intensity v corresponding to the second pixel pair correspondingto V₀. So, vector p₁′ and vector p₂′ can be specified as:

p ₁′=(u ₁ ′,v ₁′)  (12)

p ₂′=(u ₂ ′,v ₂′)  (13)

So, now in the linear context described above and referring to equation(4), an overlay value of the first overlay of interest can then bedefined based on U₀,V₀, and vectors p₁′ and p₂′ as follows:

$\begin{matrix}{{OV}_{\underset{\_}{p_{1}}} = {{\left( {{u_{1}^{\prime}U_{0}} + {v_{1}^{\prime}V_{0}}} \right)/\cos}\theta_{1}}} & (14)\end{matrix}$

Additionally or alternatively, an overlay value of the second overlay ofinterest can then be defined based on U₀, V₀ and vectors p₁′ and p₂′ asfollows

$\begin{matrix}{{OV}_{\underset{\_}{p_{2}}} = {{\left( {{u_{2}^{\prime}U_{0}} + {v_{2}^{\prime}V_{0}}} \right)/\cos}\theta_{2}}} & (15)\end{matrix}$

So, from equation (14), the weights to determine the first overlay ofinterest are, for respectively U₀ and V₀, the following:

$\begin{matrix}{\frac{u_{1}^{\prime}}{\cos \; \theta_{1}},\frac{v_{1}^{\prime}}{\cos \; \theta_{1}}} & (11)\end{matrix}$

Further, from equation (15), the weights to determine the second overlayof interest are, for respectively U₀ and V₀, the following:

$\begin{matrix}{\frac{u_{2}^{\prime}}{\cos \; \theta_{2}},\frac{v_{2}^{\prime}}{\cos \; \theta_{2}}} & (16)\end{matrix}$

So, as will be appreciated, this can be repeated for all, orsubstantially all, of the pixel pairs in the pupil representation so asto arrive at a set of weights w_(i) for the first overlay of interest(w_(i) ¹) and/or to arrive at a set of weights w_(i) for the secondoverlay of interest (w_(i) ²). One or both of these can then applied tomeasured optical characteristic values in accordance with equation (4)to arrive at an overlay value for the respective overlay of interest. Ofcourse, one or more further overlays of interest can be evaluated andone or more appropriate weight sets determined for them. As will beappreciated, in an embodiment, the sensitivity (e.g., Jacobian) to allof the different overlays of interest is included in the weightsdefinition for a particular overlay of interest.

So, for example for a unit cell having 4 layers (with one of the layersbeing a reference layer) wherein a shift in each of the layers in the Xand Y directions could cause a change in symmetry (e.g., cause anasymmetry, or cause a further asymmetry, or cause an asymmetric unitcell to become symmetric), then 6 vectors can be created (each beingassociated with a different pixel pair), the 6 vectors comprising aX-direction overlay vector for each of the layers and a Y-directionoverlay vector for each of the layers. There could thus be 6 sets ofweights to derive the respective overlays. Of course not all of theweight sets need to be derived if one of the vectors is not of interest(but in an embodiment, the sensitivity (e.g., Jacobian) to all of thedifferent overlays of interest is included in the weights definition forthe particular overlay of interest). Any other overlay can then bedetermined by appropriate mathematical combination of two or more ofthese overlays.

As will be appreciated, some shifts of a layer in a unit cell would notcause a change in symmetry and so the overlay corresponding to thatshift cannot be determined from the unit cell. So, obviously, no vectorwould be defined for such a shift. So, taking FIG. 18 as an example,three vectors could be defined for that unit cell—one for theX-direction overlay and two for the different Y-direction overlays. So,one sets of weights can be determined that will give the overlay in theX-direction when combined with measured optical characteristic values.Or, a set of weights can be determined that will give one of theoverlays in the Y-direction when combined with measured opticalcharacteristic values and/or a set of weights can be determined thatwill give the other of the overlays in the Y-direction when combinedwith measured optical characteristic values. Of course, all three setsof weights can be determined or just two.

The discussion above has focused on a target formed by one or moreinstances of a symmetrical unit cell made up of structures of a device.Such a target can enable, through on-product measurement of radiationredirected by the on-product target, determination of an on-productvalue of a patterning process parameter. However, as described above,the target need not be made up of only device structures. In otherwords, a non-product target can be provided whose structures don'texclusively comprise device structures. For example, in an embodiment, atarget can be specially created of structures that are not used to formthe device but rather are merely used for measurement. Such a target canbe provided, e.g., in a scribe lane away from the device (and thusprovided in a part of a device patterning pattern away from the devicepattern). In an embodiment, the target can be provided in among thedevice pattern (and thus provided among the features of a device patternof a patterning device pattern). Where appropriate, a non-product targetcan comprise one or more device structures and one or more speciallycreated structures that are not used to form the device but rather aremerely used for measurement.

A non-product target can be useful if, for example, a patterning processparameter is being determined for a device pattern that cannot presentsymmetric unit cell instances. As another example, a non-product targetcan be useful if, for example, a patterning process parameter is beingdetermined for a portion of a device pattern that doesn't have asymmetrical unit cell as described above that can give a measure of thatpatterning process parameter. For example, there can be cases of astructure for overlay after etch is desired to be determined using thesymmetrical unit cell methods described above but has no symmetry. Forexample, logic circuits or structures have many process layers\stepsthat are each able to introduce a different overlay component that canbreak the symmetry of the structure. In the case of logic circuits forexample, measurement on the device pattern typically cannot be performeddue to the lack of a symmetric unit cell of logic circuit structures.

As a further example, the non-product target can be used in associationwith a device pattern that can present symmetric unit cell instances(and even if the unit cell can give a measure of all patterning processparameters of interest). This can be, for example, if the device patternis complex, which can require significant computation time. Further, thedevice pattern may present potential cross-talk with signals ofpatterning process parameters not of interest. As an example, the pupilcorrelations of different overlay components might be so large that itis impossible to separate the different overlay errors.

Thus, a non-product target can be used with a device pattern that hasinstances of a symmetrical unit cell for a beam spot or with a devicepattern that can't present instances of a symmetrical unit for the beamspot.

So, in an embodiment, a non-product target can be designed such that aparticular type of patterning process parameter (e.g., overlay) ofinterest breaks a certain type of (pupil) symmetry of the non-producttarget; this is similar to the techniques described above. And, whileoverlay will be a focus of the discussion, like as discussed above, oneor more different patterning process parameters than overlay may bedetermined.

Of course, for the non-product target to give a measure of thepatterning process parameter, the non-product target will follow thoseprocess steps that are considered to be the main contributor to thepatterning process parameter at issue. Thus, as discussed above, if,e.g., an overlay between two structures created in separate patterningprocesses are of interest, then the non-product target comprises astructure created in each of the separate patterning processes anddesirably by a same or comparable process.

Further, breaking a certain type of geometric symmetry (e.g.,Y-symmetry) leads to breaking the same type of symmetry in the pupildomain. So, a non-product target can be designed for a particular typeof geometric symmetry such that a corresponding particular patterningprocess parameter value causes a break in the symmetry. For example, aY-symmetry broken by an X-overlay. Further, where there is symmetry inmore than one direction using a target that is designed such that adifferent type of patterning process parameter (e.g., different overlaytype such as overlay in X and overlay in Y) breaks a different type ofsymmetry enables monitoring the induced asymmetry (according to therelevant type of symmetry) to determine one patterning process parameter(e.g., overlay) at a time.

A non-product target can have one or more advantages. For example, anon-product target design can have reduced or minimized pupilcorrelations compared to using a measurement of radiation from anon-product target and, as a consequence, a patterning process parameterof interest is easier to determine from the measured radiation. In anembodiment, the non-product target design can reduce or minimizecross-talk between different types of a same patterning processparameter or between different kinds of patterning process parameter.Thus, a cleaner signal can be obtained. The non-product target designcan have of advantage of measuring a patterning process parameter for adevice pattern that doesn't have instances of a symmetric unit cell fora beam spot. Thus, the non-product target design can enable theextension of the measurement and determination techniques describedherein to applications like logic and/or advanced memory where thedevice pattern may not have instances of a useful symmetric unit cell. Anon-product target design can have a relatively simplified structure,which can, e.g., make it easier for modeling as described herein. Thiscan make it easier to separate and determine more than one patterningprocess parameter type from a single target. Further, a non-producttarget design can be specially configured to determine just a singlepatterning process parameter type or determine a specific combination ofpatterning process parameter types.

But, oversimplification in a non-product target design may kill criticalcontributors to the patterning process parameter (e.g. overlay). Tomitigate this risk, the non-product target design should assume thesubstantially same process steps as the device product pattern. Further,main contributors to the patterning process parameter of interest shouldbe identified so that they can be factored into the non-product targetdesign and/or and associated modeling.

So, like an on-product target design, an embodiment of a non-producttarget design is defined in terms of a unit cell comprising structureshaving a geometric symmetry. In an embodiment, the symmetry can be in afirst direction (e.g., X-direction), in a second orthogonal direction(e.g., Y-direction), or both. In an embodiment, the unit cell is createdsuch that a change in physical configuration of the structures in theunit cell causes a break in symmetry, which break in symmetry results ina particular radiation distribution which can be processed to determinea value of a patterning process parameter of interest as describedabove. Thus, the unit cell effectively as the metrology target and, inan embodiment, contains a minimum area of structures used to provide thesignal to determine the patterning process parameter of interest.

In an embodiment, the non-product target design comprises structurescreated in at least two patterning processes (e.g., at least twoexecutions of a same type of patterning process, at least two executionsof different types of patterning processes, etc.). In an embodiment,where the plurality of patterning process executions result instructures in different layers for which a patterning process parameterof interest is being determined, the non-product target design unit cellcomprises a structure from each of the plurality of layers of interest.In an embodiment, where the patterning process executions result instructures in a same layer for which a patterning process parameter ofinterest is being determined, the non-product target design unit cellcomprises a structure from each of the applicable different patterningprocess executions of interest. In an embodiment, a first structurecreated by a first patterning process and/or a second structure createdby a second patterning process is not used to create a functional aspectof a device pattern.

So, in an embodiment and in terms of the unit cell, structures from aplurality of patterning processes together form an instance of the unitcell and the unit cell has geometric symmetry at a nominal physicalconfiguration, wherein the unit cell has a feature that causes, at adifferent physical configuration than the nominal physical configurationdue to, e.g., a relative shift in pattern placement in the firstpatterning process, the second patterning process and/or anotherpatterning process, an asymmetry in the unit cell. An example of such afeature is one that causes asymmetry in the unit cell in response to anoffset of a structure in one layer relative a structure to anotherlayer.

In an embodiment, the non-product target design comprises a repetitionof the unit cell. That is in an embodiment, a beam spot on a physicalinstance of the non-product target would illuminate a plurality ofinstances of the unit cell filling up the beam spot. In an embodiment,the non-product target design comprises at least 4 instances, at least 8instances, at least 10 instances, at least 20 instances, at least 40instances, at least 80 instances, at least 100 instances, at least 200instances, at least 400 instances, or at least 1000 instances of theunit cell.

In an embodiment, the non-product target as produced on a substrate hasa small size. For example, the non-product target can have an area of100 square microns or less, 50 square microns or less, or 25 squaremicrons or less. In an embodiment, the non-product target has across-wise dimension of 10 microns or less or 5 microns or less. In anembodiment, the beam spot for the non-product target has a cross-wisedimension smaller than the maximum cross-wise dimension of the target.In an embodiment, the beam spot for a non-product target has across-wise dimension of 10 microns or less, 5 microns or less or 2microns or less. In an embodiment, the beam spot for a non-producttarget has a cross-sectional area of less than or equal to 100 squaremicrons, 50 square microns or less, or 25 square microns or less. In anembodiment, the unit cell of a non-product target has an area of 250,000square nanometers or less, 150,000 square nanometers or less, 100,000square nanometers or less, or 50,000 square nanometers or less. In anembodiment, the unit cell of a non-product target has a cross-wisedimension of 500 nanometers or less, 300 nanometers or less, 200nanometers or less or 150 nanometers or less. In an embodiment, the unitcell of the non-product target has a smaller size than a unit cell of adevice pattern associated with the non-product target.

In an embodiment, the unit cell comprises a feature (e.g., a structure,a void (e.g., a gap), etc.) that corresponds to a feature (e.g., astructure, a void, etc.) of a device made using a first patterningprocess and a feature (e.g., a structure, a void, etc.) that correspondsto a feature (e.g., a structure, a void, etc.) of a device made using asecond patterning process. For example, a structure of the unit cell iscreated by a first patterning process that creates a correspondingdevice feature of a device and another structure of the unit cell iscreated by a second patterning process that creates a correspondingdevice feature of the device. In an embodiment, one or more featurescreated in a unit cell share key process steps of a feature in a devicefor which the unit cell feature is being used to determine a patterningprocess parameter. In an embodiment, the features of the unit cellcreated by the respective corresponding patterning processes correspondto, e.g., one or more features (e.g., structures such as lines) of thedevice that extend or are elongate in a direction essentially parallelto the features (e.g., lines) of the unit cell. So, for example, theunit cell comprises structures extending in a Y-direction can be used todetermine overlay of corresponding structures in the device extending inthe Y-direction.

In an embodiment, as described further in examples presented below, theunit cell can enable determination of multiple different types of a samepatterning process parameter (e.g., overlay). For example, a unit cellenable determination of 2 or more types of overlay, 3 or more types ofoverlay, etc. For example, besides types of overlay in differentdirections (e.g., in X and Y), the unit cell can enable determination ofoverlay between different combinations of features and/or betweendifferent combinations of layers.

In an embodiment, the unit cell has features that have comparabledimensions (e.g., widths and/or pitches) to corresponding features of adevice. Comparable dimensions means identical or within ±5% from thedevice feature dimension (i.e., 95% to 105% of the device featuredimension), within ±10% from the device feature dimension, within ±15%from the device feature dimension, within ±20% from the device featuredimension, or within ±25% from the device feature dimension. In anembodiment, the dimensions of one or more the unit cell features can beselected to improve the measurement signal and thus not match thecorresponding dimension of a feature of the device pattern. This can bedone, for example, by evaluating the sensitivity of signal output tochange in dimension of the target feature and so the dimension can beselected in the particular circumstance to maximize signal or provide asignal meeting or crossing a threshold.

In an embodiment, the non-product target can be used in conjunction withan on product target. For example, an overlay can be determined usingthe non-product target and the result can be fed-forward todetermination of the overlay using an on-product target.

Referring to FIG. 21, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 21A, an example of a unit cell 2000 isdepicted. The unit cell 2000 comprises a structure 2010 (in this case, aplurality of lines 2010) created in a first patterning process and astructure 2020 (in this case, a second plurality of lines 2020) createdin a second patterning process. An anchor 2030 is depicted to show thesymmetry of the unit cell. In this case, the unit cell 2000 has asymmetry in the Y direction. FIG. 21A shows the unit cell in symmetricform, and would correspond to a certain nominal overlay value (e.g.,zero overlay).

In an embodiment, the structure 2010 corresponds to a feature of adevice made using the first patterning process. That is, the structure2010 is to be created by a first patterning process that creates acorresponding device feature of a device. For example, the creation ofthe structure 2010 corresponds to a comparable creation of a structurein a device. Similarly, in an embodiment, the structure 2020 correspondsto a feature of the device made using the second patterning process.That is, the structure 2020 is to be created by a second patterningprocess that creates a corresponding device feature of the device. Forexample, the creation of the structure 2020 corresponds to a comparablecreation of a structure in the device. So, in an embodiment, thestructure 2010 corresponds to, e.g., one or more features (e.g.,structures such as lines) of the device that extend in a directionessentially parallel to the features (e.g., lines) of structure 2010.Similarly, the structure 2020 corresponds to, e.g., one or more features(e.g., structures such as lines) of the device that extend in adirection essentially parallel to the features (e.g., lines) ofstructure 2020. In an embodiment, the structure 2010 is created in adifferent layer than structure 2020. So, in an embodiment, thestructures 2010 and 2020 extending in the Y-direction can be used todetermine overlay of corresponding structures in the device extending inthe Y-direction.

As noted above, in an embodiment, the structures 2010 and 2020 havecomparable widths and/or pitches to features of a device. For example,the structure 2010 has a comparable width and/or pitch to features of acorresponding device structure created in the first patterning process.Similarly, for example, the structure 2020 has a comparable width and/orpitch to features of a corresponding device structure created in thesecond patterning process.

In unit cell 2000, a feature that will cause a break in symmetry for adifferent physical configuration of the structures in the unit cell 2000is a physical difference between the structure 2010 and the structure2020. In an embodiment, the difference is a difference in width ofstructures 2010 and 2020 in the X-direction as schematically depicted inFIG. 21A. In an embodiment, the difference is a difference in materialcomposition of structure 2010 and 2020, e.g., structure 2010 is made ofa different material than structure 2020. In an embodiment, there can bea combination of physical differences, e.g., difference in width andphysical composition.

The result of the physical difference in the case of unit cell 2000 isthat a relative shift 2040 in the X-direction in an X-Y plane betweenstructures 2010 and 2020 causes asymmetry in the unit cell 2000. This isdepicted in FIG. 21B. In FIG. 21B, structure 2010 shifts from itsnominal (e.g., design) position of structure 2010 shown in FIG. 21A whenit is created in the second patterning process. The result is adisplacement 2050 from the anchor 2030. Thus, assuming that the unitcell 2000 corresponds to a situation of no overlay, the displacement2050 corresponds to an overlay that is desirably determined byprocessing the radiation redirected by the target comprising unit cell2000 as described above (e.g., the weights and pupil distributions).

Since unit cell 2000 shows asymmetry with respect to the Y axis, thetranslation in the X-direction in combination with the asymmetry causingfeature (here the physical difference between structures 2010 and 2020)yields a radiation distribution from which an X-overlay value can bedetermined. In an embodiment, that X-overlay value would correspond toan X-overlay of features of a device made using the respectivepatterning processes. Now, of course, the unit cell 2000 can beeffectively rotated 90 degrees about the anchor 2030 to give a Y-overlayvalue for a relative shift in the Y-direction between structure 2010 and2020. In an embodiment, that Y-overlay value would correspond to aY-overlay of features of a device made using the respective patterningprocesses. In an embodiment, in that case, the device featurescorresponding to structures 2010 and 2020 would extend in theX-direction.

So, in an embodiment, the structures 2010 and 2020 of the unit cellcorrespond to respective features of a device that extend in a samedirection. As a result, the structures of unit cell 2000 can yield avalue of overlay in a direction orthogonal to a direction ofextension/elongation of features of a device. Thus, by identifyingdevice features extending in a same direction for which an overlay in anorthogonal direction is of interest, the unit cell 2000 can be designedto mimic the overlay by appropriate selection of structures 2010 and2020 and causing their creation with the creation of the devicefeatures.

In FIG. 21, the unit cell 2000 was designed to primarily determine theoverlay between the formation of the structures (e.g., lines)themselves. In some patterning processes, a particular pattern istransferred to a substrate having a structure such that, when etching isperformed with respect to that pattern, a portion of the structure isremoved. This process and its result will be herein referred to as acut. For example, a device structure (e.g., a line) can be cut into aplurality of pieces and/or an end portion of a device structure can becut off. As will be appreciated, it can be desirable to know whether acut has been accurately made. Thus, it can be desirable to know theoverlay between cuts and/or the overlay between a cut and a structure.

Furthermore, the unit cell of FIG. 21 enables determining a value ofoverlay in a direction orthogonal to a direction of extension/elongationof features of a device. But, it can be desirable to determine anoverlay in a direction parallel to the direction of extension/elongationof the features of a device.

Referring now to FIG. 22, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 22A, an example of a unit cell 2100 isdepicted. The unit cell 2100 comprises a structure 2110 (in this case, aplurality of lines 2110) and a structure 2120 (in this case, a secondplurality of lines 2120). As will be described in more detail below, inthis embodiment, overlay in X and in Y can be determined from thisnon-product target design.

In the embodiment here, the unit cell 2100 has features of unit cell2000 of FIG. 21 and thus can enable determination of X direction overlayas described above if structure 2110 is created in a first patterningprocess and the structure 2120 is created in a second patterning processand there is a physical difference between structure 2110 and 2120.However, if, e.g., X direction overlay is not desired then structures2110 and 2120 can be created in the same patterning process and/orstructures 2110 and 2120 can have the same physical characteristic,i.e., do not have a physical difference. But, even if X directionoverlay is not desired, structures 2110 and 2120 can have a differentphysical characteristic to provide a better measurement signal.

So, in this embodiment that enables determining overlay in X and in Y,the unit cell 2100 comprises a structure 2110 created in a firstpatterning process and a structure 2120 created in a second patterningprocess. An anchor 2130 is depicted to show the symmetry of the unitcell. In this case, the unit cell 2100 has a symmetry in the Y directionand a symmetry in the X direction. FIG. 22A shows the unit cell insymmetric form, and would correspond to a certain nominal overlay value(e.g., zero overlay).

In an embodiment, the structure 2110 corresponds to a feature of adevice made using the first patterning process as described above andthe structure 2120 corresponds to a feature of the device made using thesecond patterning process. And, in unit cell 2100, a feature that willcause a break in symmetry for a different physical configuration of thestructures in the unit cell 2100 is a physical difference between thestructure 2110 and the structure 2120. In an embodiment, the differenceis a difference in width of structures 2110 and 2120 in the X-directionas schematically depicted in FIG. 22A. In an embodiment, the differenceis a difference in material composition of structure 2110 and 2120,e.g., structure 2110 is made of a different material than structure2120.

As discussed above, the result of the physical difference in the case ofunit cell 2100 is that a relative shift 2180 in the X-direction in anX-Y plane between structures 2110 and 2120 causes asymmetry in the unitcell 2100. This is depicted in FIG. 22C. In FIG. 22C, structure 2110shifts from its nominal (e.g., design) position of structure 2110 shownin FIG. 22A when it is created in the second patterning process. Theresult is a displacement 2190 from the anchor 2130. Thus, assuming thatthe unit cell 2100 corresponds to a situation of no overlay, thedisplacement 2190 corresponds to an overlay that is desirably determinedby processing the radiation redirected by the target comprising unitcell 2100 as described above (e.g., the weights and pupildistributions).

Since unit cell 2100 shows asymmetry with respect to the Y axis, thetranslation in the X-direction in combination with the asymmetry causingfeature (here the physical difference between structures 2110 and 2120)yields a radiation distribution from which an X-overlay value can bedetermined. In an embodiment, that X-overlay value would correspond toan X-overlay of features of a device made using the respectivepatterning processes. Now, of course, the unit cell 2100 can beeffectively rotated 90 degrees about the anchor 2130 to give a Y-overlayvalue for a relative shift in the Y-direction between structure 2110 and2120. In an embodiment, that Y-overlay value would correspond to aY-overlay of features of a device made using the respective patterningprocesses. In an embodiment, in that case, the device featurescorresponding to structures 2110 and 2120 would extend in theX-direction.

Now, unit cell 2100 further enables determination of an overlay in the Ydirection. Similarly to how the structures in a unit cell of anon-product target can correspond to a feature in a device, a cut in anon-product target design can correspond to a feature (e.g., a cut) in adevice.

Referring to FIG. 22A, the unit cell 2100 comprises a cut 2150 createdin a first patterning process and a cut 2140 created in a secondpatterning process. The cuts 2150 and 2140 are arranged so as tomaintain symmetry in the unit cell in a nominal physical configuration.

In an embodiment, the cut 2150 corresponds to a feature of a device madeusing the first patterning process. That is, the cut 2150 is to becreated by a first patterning process that creates a correspondingdevice feature of a device. For example, the creation of the cut 2150corresponds to a comparable creation of a cut in a device. Similarly, inan embodiment, the cut 2140 corresponds to a feature of the device madeusing the second patterning process. That is, the cut 2140 is to becreated by a second patterning process that creates a correspondingdevice feature of the device. For example, the creation of the cut 2140corresponds to a comparable creation of a cut in the device. So, in anembodiment, the cut 2150 corresponds to, e.g., one or more features(e.g., one or more cuts) of the device that extend in a directionessentially parallel to the cut 2150. Similarly, the cut 2140corresponds to, e.g., one or more features (e.g., one or more cuts) ofthe device that extend in a direction essentially parallel to the cut2140. In an embodiment, the cut 2150 is created in a different layerthan cut 2140. So, in an embodiment, the cuts 2150 and 2140 can be usedto determine overlay of corresponding cuts in the device in theY-direction.

In an embodiment, the cuts 2150 and 2140 have comparable widths and/orpitches to features of a device. For example, the cut 2150 has acomparable width and/or pitch to features (e.g., one or more cuts) of acorresponding device structure created in the first patterning process.Similarly, for example, the cut 2140 has a comparable width and/or pitchto features (e.g., one or more cuts) of a corresponding device structurecreated in the second patterning process.

In unit cell 2100, a feature that will cause a break in symmetry for adifferent physical configuration of the structures in the unit cell 2100is the arrangement of cuts 2150 and 2140 that will create asymmetry uponrelative shift between cuts 2150 and 2140. In an embodiment, the cut2140 is made in each structure 2120, while cut 2150 is not made in eachstructure 2110. As will be appreciated, the cut 2150 can be made in eachstructure 2110, while cut 2140 is not made in each structure 2120. Aswill be appreciated, many different variations are possible in terms ofthe cuts including different locations of the cuts and/or differentsizes of the cuts.

The result of the arrangement of cuts 2150 and 2140 is that a relativeshift 2160 in the Y-direction in an X-Y plane between cuts 2150 and 2140causes asymmetry in the unit cell 2100. This is depicted in FIG. 22B. InFIG. 22B, cut 2150 shifts from its nominal (e.g., design) position shownin FIG. 22A when it is created in the first patterning process. Theresult is a displacement 2170 from the anchor 2130. Thus, assuming thatthe unit cell 2100 corresponds to a situation of no overlay, thedisplacement 2170 corresponds to an overlay that is desirably determinedby processing the radiation redirected by the target comprising unitcell 2100 as described above (e.g., the weights and pupildistributions).

Since unit cell 2100 shows asymmetry with respect to the X axis, thetranslation in the Y-direction in combination with the asymmetry causingfeature (here the arrangement of cuts 2140 and 2150) yields a radiationdistribution from which a Y-overlay value can be determined. In anembodiment, that Y-overlay value would correspond to a Y-overlay offeatures of a device made using the respective patterning processes.Now, of course, the unit cell 2100 can be effectively rotated 90 degreesabout the anchor 2130 to give an X-overlay value for a relative shift inthe X-direction between cuts 2140 and 2150. In an embodiment, thatX-overlay value would correspond to an X-overlay of features (e.g.,cuts) of a device made using the respective patterning processes. In anembodiment, in that case, the device features (e.g., cuts) correspondingto cuts 2140 and 2150 would extend in the X-direction.

So, in an embodiment, the cuts 2140 and 2150 of the unit cell correspondto respective features of a device that extend in a same direction. As aresult, the structures of unit cell 2100 can yield a value of overlay ina direction parallel to a direction of extension/elongation of featuresof a device. Thus, by identifying device features extending in a samedirection for which an overlay in a parallel direction is of interest,the unit cell 2100 can be designed to mimic the overlay by appropriateselection of cuts 2140 and 2150 and causing their creation with thecreation of the device features.

As noted above, in an embodiment, the cuts 2140 and 2150 can be createdin the structures 2110 and 2120 in a similar manner as cuts are made indevice features. Thus, the cuts 2140 and 2150 can give a good measure ofthe overlay of cuts made in creating device structures. But, in anembodiment, the cuts 2140 and 2150 may instead be voids created whenstructure 2110 and 2120 are created and can be created as part ofcorresponding patterning process to create structures of a device. Thus,voids 2140 and 2150 in this case can give a good measure of the overlayof structures made in creating the device.

And, while FIG. 22 shows cuts/voids facilitating determination ofoverlay, the structures 2110 and 2120 could have one or more protrusionsor deformities, e.g., protrusions at the locations of the depicted cuts.So, relative displacement between such protrusions or deformities couldcause asymmetry in the unit cell much like the cuts 2140 and 2150. Theprotrusions or deformities can be created when the structures 2110 and2120 are created or created by a cutting process. Thus, the protrusionsor deformities can be used to facilitate, e.g., determination of overlaybetween device structures (e.g., for protrusions or deformities createdwhen the structures 2110 and 2120 are created) or between device cuts(e.g., for protrusions or deformities created by cutting structures 2110and 2120).

FIG. 22D schematically depicts a non-product target comprising aplurality of instances of the unit cell. In this non-limiting example,FIG. 22D comprises at least 4 instances of the unit cell. FIG. 22D showsthe instances of the unit cell in symmetric form, and would correspondto a certain nominal overlay value (e.g., zero overlay). In anembodiment, the pitch 2192 of structures 2110 is comparable to the pitch2194 of structure 2120.

In FIG. 22D, if, e.g., the second patterning process is not well alignedin the X-direction resulting in a relative shift between structures 2110and 2120, the Y-symmetry is broken, and so is the Y-symmetry in thepupil. Thus, measurement of the target in that condition can translateinto an X-overlay determination. Effectively, the structures 2110 and2120 are used to determine X-overlay. Similarly, if, e.g., the secondpatterning process is not well aligned in the Y-direction resulting in arelative shift between cuts 2140 and 2150, the X-symmetry is broken andso is the X-symmetry in the pupil. Thus, measurement of the target inthat condition can translate into a Y-overlay determination.Effectively, the cuts 2140 and 2150 are used to determine Y-overlay.Further, as seen in FIG. 22D, a shift of a cut in the Y direction doesnot change the symmetry with respect to the Y axis and shift of thestructures in the X direction does not change the symmetry with respectto the X axis. Thus, the X and Y direction overlays are decoupled. So,while a combination of a badly aligned patterning process in X- andY-directions results in broken X- and Y-symmetry, the different overlayscan be separated from the signal.

In an embodiment, the number of structures and their sizes, pitches,etc. can be configured to closely comparable to the patterning processesof the device pattern. Similarly, the number of cuts (orprotrusions/deformities) and their sizes, pitches, etc. can beconfigured to closely comparable to the patterning processes of thedevice pattern. For example, cuts will be comparable to the CD and pitchas used in the device when possible. But, in an embodiment, thelocations and/or number of cuts are adapted to make a symmetric unitcell. Further, the non-product target overlay sensitivity can betailored by adapting the pitch of structures and cuts (orprotrusions/deformities).

Referring to FIG. 23, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 23A, an example of a unit cell 2300 isdepicted. The unit cell 2300 comprises a structure 2310 (in this case, aplurality of lines 2310) and a structure 2320 (in this case, a secondplurality of lines 2320). Different from FIGS. 21 and 22, structure 2310extends in a direction substantially perpendicular to structure 2320. Ananchor 2340 is depicted to show the symmetry of the unit cell. In thiscase, the unit cell 2300 has a symmetry in the Y direction. FIG. 23Ashows the unit cell in symmetric form, and would correspond to a certainnominal overlay value (e.g., zero overlay).

So, in this embodiment of unit cell 2300, an overlay in the X-directionbetween a structure extending a first direction and a cut or a structureextending a second direction essentially orthogonal to the firstdirection can be determined from the redirected radiation from this unitcell.

In particular, similar to the principles described above, the unit cell2300 comprises a structure 2310 created in a first patterning processand comprise a cut 2330 and/or a structure 2320 created in a secondpatterning process. Where, for example, the overlay between thestructure 2310 and the cut 2330 is desired then the structure 2310 iscreated in the first patterning process and the cut 2330 is made in thesecond patterning process (optionally, the structure 2320 is alsocreated in the second patterning process). Where, for example, theoverlay between the structures 2310 and 2320 is desired then thestructure 2310 is created in the first patterning process and thestructure 2320 is created in the second patterning process with a voidcomparable to, e.g., cut 2330. The structures 2310 and 2320 and the cut2330 are arranged so as to maintain symmetry in the unit cell in anominal physical configuration.

Similar to embodiments described above, the structure 2310 correspondsto a feature of a device made using the first patterning process. Thatis, the structure 2310 is to be created by a first patterning processthat creates a corresponding device feature of a device. For example,the creation of the structure 2310 corresponds to a comparable creationof a structure in a device. Similarly, in an embodiment, the structure2320 and/or cut 2330 corresponds to a feature of the device made usingthe second patterning process. That is, the structure 2320 and/or cut2330 are to be created by a second patterning process that creates acorresponding device feature of the device. For example, the creation ofthe cut 2330 corresponds to a comparable creation of a cut in thedevice. So, in an embodiment, the structure 2310 corresponds to, e.g.,one or more features (e.g., one or more structures) of the device thatextend in a first direction essentially parallel to the structure 2310.Similarly, the structure 2320 and/or cut 2330 correspond to, e.g., oneor more features of the device that extend in a second directionessentially perpendicular to the first direction. In an embodiment, thestructure 2320 and/or cut 2330 is created in a different layer thanstructure 2310. So, in an embodiment, the cut 2330 (or a void comparableto the cut of structure 2320) can be used to determine overlay ofcorresponding features in the device in the X-direction.

In an embodiment, the structure 2310 and the structure 2320 and/or cut2330 have comparable widths and/or pitches to features of a device. Forexample, the structure 2310 has a comparable width and/or pitch tofeatures (e.g., one or more structures) of a corresponding devicestructure created in the first patterning process. Similarly, forexample, the structure 2320 and/or cut 2330 have a comparable widthand/or pitch to features of a corresponding device structure created inthe second patterning process.

In unit cell 2300, a feature that will cause a break in symmetry for adifferent physical configuration of the structures in the unit cell 2300is the arrangement of cut 2330 (or the comparable void in a structure2320) that will create asymmetry upon a relative shift between thestructure 2310 and the cut 2330 (or between structure 2310 and 2320). Aswill be appreciated, many different variations are possible in terms ofthe cuts/voids including different locations of the cuts/voids and/ordifferent sizes of the cuts/voids.

The result of the arrangement of cut 2330 (or void 2330) in combinationwith the essentially perpendicular structures 2310 and 2320 is that arelative shift 2350 in the X-direction in an X-Y plane between structure2310 and cut 2330 (or between structures 2310 and 2320 where there is avoid) causes asymmetry in the unit cell 2300. This is depicted in FIG.23B. In FIG. 23B, cut 2330 shifts from its nominal (e.g., design)position shown in FIG. 23A when it is created in the second patterningprocess. The result is a displacement 2360 from the anchor 2340. Thus,assuming that the unit cell 2300 corresponds to a situation of nooverlay, the displacement 2360 corresponds to an overlay that isdesirably determined by processing the radiation redirected by thetarget comprising unit cell 2300 as described above (e.g., the weightsand pupil distributions).

Since unit cell 2300 shows asymmetry with respect to the Y axis, thetranslation in the X-direction in combination with the asymmetry causingfeature (here the arrangement of cut 2330 (or void 2330) in combinationwith the essentially perpendicular structures 2310 and 2320) yields aradiation distribution from which a X-overlay value can be determined.In an embodiment, that X-overlay value would correspond to an X-overlayof features of a device made using the respective patterning processes.

So, in an embodiment, the structure 2310 and the structure 2320 and/orcut 2330 of the unit cell correspond to respective features of a devicethat extend in a same direction. As a result, the structures of unitcell 2300 can yield a value of overlay for features that extend or areelongate in perpendicular directions. Thus, by identifying devicefeatures extending in orthogonal direction for which an overlay in acertain direction is of interest, the unit cell 2300 can be designed tomimic the overlay by appropriate selection of the cut 2330 (or void2330) in relation to orthogonal structures 2310 and 2320 and causingtheir creation with the creation of the device features.

And, while FIG. 23 shows cuts/voids facilitating determination ofoverlay, the structures 2310 and 2320 could have one or more protrusionsor deformities, e.g., protrusions at the locations of the depicted cuts.So, relative displacement between such protrusions or deformities couldcause asymmetry in the unit cell much like the cut 2330. The protrusionsor deformities can be created when the structures 2310 and 2320 arecreated or created by a cutting process. Thus, the protrusions ordeformities can be used to facilitate, e.g., determination of overlaybetween device structures (e.g., for protrusions or deformities createdwhen the structures 2310 and 2320 are created) or between a cut and astructure.

Now, of course, the unit cell 2300 can be effectively rotated 90 degreesabout the anchor 2340 to give a Y-overlay value for a relative shift inthe Y-direction between the structure 2310 and the structure 2320 and/orcut 2330. In an embodiment, that Y-overlay value would correspond to aY-overlay of features of a device made using the respective patterningprocesses.

Referring to FIG. 24, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 24A, an example of a unit cell 2400 isdepicted. The unit cell 2400 comprises a structure 2410 (in this case, aplurality of lines 2410) and a structure 2420 (in this case, a secondplurality of lines 2420). Structure 2410 extends in a directionsubstantially perpendicular to structure 2420. An anchor 2440 isdepicted to show the symmetry of the unit cell. In this case, the unitcell 2400 has a symmetry in the X direction. FIG. 24A shows the unitcell in symmetric form, and would correspond to a certain nominaloverlay value (e.g., zero overlay).

So, in this embodiment of unit cell 2400, an overlay in the Y-directionbetween a structure extending a first direction and a cut or a structureextending a second direction essentially orthogonal to the firstdirection can be determined from the redirected radiation from this unitcell.

FIG. 24 is effectively a reverse arrangement of FIG. 23. While FIG. 23is designed for determining X direction overlay, FIG. 24 is designed todetermine Y direction overlay; however, like FIG. 23, the FIG. 24 unitcell can be rotated 90 degrees to determine X direction overlay. But,differently than FIG. 23, a cut 2430 (or a void 2430 of createdstructure 2410) is created in the first patterning process compared tothe second patterning process in the embodiment of FIG. 24.

So, in unit cell 2400, a feature that will cause a break in symmetry fora different physical configuration of the structures in the unit cell2400 is the arrangement of cut 2430 (or the comparable void in astructure 2410) that will create asymmetry upon a relative shift betweenthe cut 2430 and the structure 2420 (or between structures 2410 and2420). As will be appreciated, many different variations are possible interms of the cuts/voids including different locations of the cuts/voidsand/or different sizes of the cuts/voids.

The result of the arrangement of cut 2430 (or void 2430) in combinationwith the essentially perpendicular structures 2410 and 2420 is that arelative shift 2450 in the Y-direction in an X-Y plane between the cut2430 and the structure 2420 (or between structures 2410 and 2420 wherethere is a void) causes asymmetry in the unit cell 2400. This isdepicted in FIG. 24B. In FIG. 24B, cut 2430 shifts from its nominal(e.g., design) position shown in FIG. 24A when it is created in thefirst patterning process. The result is a displacement 2460 from theanchor 2440. Thus, assuming that the unit cell 2300 corresponds to asituation of no overlay, the displacement 2460 corresponds to an overlaythat is desirably determined by processing the radiation redirected bythe target comprising unit cell 2400 as described above (e.g., theweights and pupil distributions).

Since unit cell 2400 shows asymmetry with respect to the X axis, thetranslation in the Y-direction in combination with the asymmetry causingfeature (here the arrangement of cut 2430 (or void 2430) in combinationwith the essentially perpendicular structures 2410 and 2420) yields aradiation distribution from which a Y-overlay value can be determined.In an embodiment, that Y-overlay value would correspond to a Y-overlayof features of a device made using the respective patterning processes.

And, while FIG. 24 shows cuts/voids facilitating determination ofoverlay, the structures 2410 and 2420 could have one or more protrusionsor deformities, e.g., protrusions at the locations of the depicted cuts.So, relative displacement between such protrusions or deformities couldcause asymmetry in the unit cell much like the cut 2430. The protrusionsor deformities can be created when the structures 2410 and 2420 arecreated or created by a cutting process. Thus, the protrusions ordeformities can be used to facilitate, e.g., determination of overlaybetween device structures (e.g., for protrusions or deformities createdwhen the structures 2410 and 2420 are created) or between a cut and astructure.

Now, of course, the unit cell 2400 can be effectively rotated 90 degreesabout the anchor 2440 to give an X-overlay value for a relative shift inthe X-direction between the structure 2410 and/or cut 2430 and thestructure 2420. In an embodiment, that X-overlay value would correspondto an X-overlay of features of a device made using the respectivepatterning processes.

Referring to FIG. 25, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 25A, an example of a unit cell 2500 isdepicted. The unit cell 2500 comprises a structure 2510 (in this case, aplurality of lines 2510) created in a first patterning process and astructure 2520 (in this case, a second plurality of lines 2520) createdin a second patterning process. Structure 2510 extends in a directionsubstantially parallel to structure 2520. An anchor 2530 is depicted toshow the symmetry of the unit cell. In this case, the unit cell 2500 hasa symmetry in the Y direction. FIG. 25A shows the unit cell in symmetricform, and would correspond to a certain nominal overlay value (e.g.,zero overlay).

The non-product target design of FIG. 25 is comparable to thenon-product target design of FIG. 21. The difference is that a centerline 2510 is not provided compared to a center line 2010 provided inFIG. 20. This means the unit cell 2500 and the non-product targetinvolves fewer structures than FIG. 20, which can, e.g., improve therelated modeling. However, this may involve a different pitch in thelines from corresponding features in the device, e.g., the pitch for thelines of structure 2520 may need to be different than a pitch ofcomparable lines in the device.

In an embodiment, structure 2510 comprises at least two sub-structures(e.g., line-like structures). Alternatively or additionally, structure2520 comprises at least two sub-structures (e.g., line-like structures).This is to enable a sufficient signal. This principle can apply to otherembodiments described herein.

Like FIG. 21, a feature that causes a break of symmetry is a physicaldifference between structures 2510 and 2520, which in the depictedembodiment is a difference in width of the structures 2510 and 2520. Andso, like FIG. 21 and as shown in FIG. 25B, a relative shift 2540 betweenthe structures 2510 and 2520 results in a break of symmetry in theY-direction. The break of symmetry results in a particular radiationdistribution that enables determination of the relative displacement2550. The relative displacement 2550 can correspond to an X directionoverlay of corresponding device features.

Referring to FIG. 26, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 26A, an example of a unit cell 2600 isdepicted. The unit cell 2600 comprises a structure 2610 (in this case, aplurality of lines 2610) created in a first patterning process and astructure 2620 (in this case, a second plurality of lines 2620) createdin a second patterning process. Structure 2610 extends in a directionsubstantially parallel to structure 2620. Further, structure 2610comprises a cut 2630 created by a patterning process and structure 2620comprises a cut 2640 created by a patterning process. An anchor 2650 isdepicted to show the symmetry of the unit cell. In this case, the unitcell 2600 has a symmetry in the Y direction and a symmetry in the Xdirection. FIG. 26A shows the unit cell in symmetric form, and wouldcorrespond to a certain nominal overlay value (e.g., zero overlay).

The non-product target design of FIG. 26 is comparable to thenon-product target design of FIG. 22 in layout and in terms of beingcapable of being used to determine overlay in X and Y directions. Adifference is that a center line 2610 is not provided compared to acenter line 2010 provided in FIG. 20. This means the unit cell 2600 andthe non-product target involves fewer structures than FIG. 20, whichcan, e.g., improve the related modeling. Further, the cuts 2630 and 2640have a different arrangement than in FIG. 22. The arrangement of cuts isto provide asymmetry but then also enable a break of symmetry when thereis a relative shift involving the cuts.

As a result of this different arrangement of FIG. 26, the design mayinvolve a different pitch in the lines from corresponding features inthe device, e.g., the pitch for the lines of structure 2620 may need tobe different than a pitch of comparable lines in the device.

Like FIG. 22, a feature that causes a break of symmetry is a physicaldifference between structures 2610 and 2620, which in the depictedembodiment is a difference in width of the structures 2610 and 2620. Andso, like FIG. 22 and as shown in FIG. 26C, a relative shift 2670 betweenthe structures 2610 and 2620 results in a break of symmetry in theY-direction. The break of symmetry results in a particular radiationdistribution that enables determination of the relative displacement2680. The relative displacement 2680 can correspond to an X directionoverlay of corresponding device features.

Further, like FIG. 22, a feature that causes a break of symmetry is thearrangement of cuts 2630 and 2640. And so, like FIG. 22 and as shown inFIG. 26B, a relative shift 2650 between the cuts 2630 and 2640 resultsin a break of symmetry in the X-direction. The break of symmetry resultsin a particular radiation distribution that enables determination of therelative displacement 2660. The relative displacement 2660 cancorrespond to a Y direction overlay of corresponding device features.

Referring to FIG. 27, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 27A, an example of a unit cell 2700 isdepicted. The unit cell 2700 comprises a structure 2710 (in this case, aplurality of lines 2710) created in a first patterning process, astructure 2720 (in this case, a second plurality of lines 2720) createdin a second patterning process, and a structure 2730 (in this case, athird plurality of lines 2730) created in a third patterning process.Structure 2710 extends in a direction substantially parallel tostructure 2720. Further, structure 2730 extends in a directionsubstantially perpendicular to structures 2710 and 2720. Further,structure 2710 comprises a cut 2740 created by a patterning process anda cut 2750 created by a patterning process. An anchor 2750 is depictedto show the symmetry of the unit cell. In this case, the unit cell 2700has a symmetry in the Y direction and a symmetry in the X direction.FIG. 27A shows the unit cell in symmetric form, and would correspond toa certain nominal overlay value (e.g., zero overlay).

The non-product target design of FIG. 27 is comparable to thenon-product target design of FIG. 22 in layout and in terms of beingcapable of being used to determine overlay in X and Y directions. Adifference is that a further structure 2730 is provided in a thirdpatterning process.

Due this arrangement, this non-product target can enable, for example,determining overlay between features across more than 2 layers of thedevice; for example, this non-product target can enable determining anoverlay between a feature in a first layer of the device and a featurein a second layer of the device and an overlay between the feature inthe first layer of the device and a feature in a third layer of thedevice.

For example, as described with respect to FIG. 22, a shift betweenstructures 2710 and 2720 in the X direction can enable determination ofan X direction overlay between device features corresponding tostructures 2710 and 2720.

But, in addition to the arrangement of FIG. 22, a shift between cut 2750and structure 2730 in the Y direction can enable determination of a Ydirection overlay between device features corresponding to cut 2750 andstructure 2730. And, in this embodiment, structure 2730 can be in adifferent layer than structure 2710 and 2720.

A feature that causes a break of symmetry in respect of structure 2730is the arrangement of cut 2750 in relation to structure 2730. And so, asshown in FIG. 27B, a relative shift 2760 between the structure 2730 andcut 2750 results in a break of symmetry in the X-direction. The break ofsymmetry results in a particular radiation distribution that enablesdetermination of the relative displacement 2770. The relativedisplacement 2670 can correspond to a Y direction overlay ofcorresponding device features.

Thus, FIG. 27 represents a combined target that enables measurement ofoverlay between 3 different process steps. The target enables, forexample, a 1^(st) layer feature to 2^(nd) layer feature overlaymeasurement (in the X direction) and 1^(st) layer feature to 3^(rd)layer feature overlay measurement (in the Y-direction). Of course, in anembodiment, the target of FIG. 27 can be separated into discrete targets(e.g., a target having structures 2710 and 2720 and cut 2740 for a1^(st) layer feature to 2^(nd) layer feature overlay measurement andanother target having structures 2710 and 2730 and cut 2740 for a 1^(st)layer feature to 3^(rd) layer feature overlay measurement) to provideone target per layer pair rather than a combined target as shown in FIG.27.

Referring to FIG. 28, a non-limiting example of a unit cell of anon-product target design is depicted for determining a patterningprocess parameter using the measuring techniques described herein (e.g.,the weights and pupil distributions). In this case, the unit cell is fordetermining overlay. In FIG. 28A, an example of a unit cell 2800 isdepicted. The unit cell 2800 comprises a structure 2810 (in this case, aplurality of closed curves 2810, e.g., essentially circles or ovals)created in a first patterning process and a structure 2820 (in thiscase, a second plurality of closed curves 2820, e.g., essentiallycircles or ovals) created in a second patterning process. Structure 2810extends in a direction substantially parallel to structure 2820. In thiscase, the unit cell 2800 has a symmetry in the Y direction and asymmetry in the X direction. FIG. 28A shows the unit cell in symmetricform, and would correspond to a certain nominal overlay value (e.g.,zero overlay).

In this arrangement, as shown in FIG. 28B, a relative shift 2830 betweenthe structures 2810 and 2820 results in a break of symmetry in theY-direction. The break of symmetry results in a particular radiationdistribution that enables determination of the relative displacement2840. The relative displacement 2840 can correspond to an X directionoverlay of corresponding device features.

Further, in this arrangement, as shown in FIG. 28C, a relative shift2850 between the structures 2810 and 2820 results in a break of symmetryin the X-direction. The break of symmetry results in a particularradiation distribution that enables determination of the relativedisplacement 2860. The relative displacement 2860 can correspond to a Ydirection overlay of corresponding device features.

A feature that causes a break of symmetry is the staggered arrangementof structure 2810 with respect to structure 2820. While, in thisembodiment, structures 2810 are depicted as having a different widththan structures 2820, it need not have such a difference where thestructures 2810 and 2820 are in a staggered arrangement as shown.Otherwise, if the structures 2810 and 2820 are not in a staggeredarrangement, a physical difference (e.g., different width, differentmaterial, etc.) could be used to break symmetry.

Different combinations of features from FIGS. 21-28 can be combined intoa unit cell to enable determination of multiple types of a parameter(e.g., X direction overlay and Y direction overlay, overlay betweendifferent combinations of features of a device, etc.). In an embodiment,separate targets can be created each for a single type of parameter(e.g., a target for X direction overlay and a separate target for Ydirection overlay, a target for overlay between a first combination offeatures and a separate target for overlay between a second combinationof features, etc.) or multiples targets can be created to determinecombinations of types of parameter.

Referring now to FIG. 29, FIG. 29A schematically depicts an example ofdevice pattern features. For example, the device pattern features couldbe for a memory device (e.g. a SRAM). As will be appreciated, a fullmemory device would likely have many more features in the area depicted.However, it may be desired to determine overlay of a certain combinationof the device pattern features depicted in FIG. 29A. Such overlay can beused for patterning process control, defect prediction in the patterningprocess, etc. as discussed in more detail herein.

In FIG. 29A, the device pattern comprises a plurality of line features2900 extending substantially parallel to each other. Further, the devicepattern comprises a plurality of line features 2910 extendingsubstantially parallel to each other and which interleave with the linefeatures 2900. In an example embodiment of a multi-patterning process asdescribed further hereafter, the features 2900 are created first andthen features 2910 are created thereafter because of, e.g., resolutionlimits.

Further, it is desired to have, e.g., multiple segments along a linefeature 2900. So, in a multi-patterning process, such segments can becreated by cuts as described above. So, the device pattern comprises aplurality of cut features 2920 with respect to line features 2900.Further, the device pattern comprises a plurality of cut features 2930with respect to line feature 2910.

The device pattern features can then be created by a plurality oflitho-etch (LE) processes. FIG. 29B, FIG. 29C, FIG. 29D and FIG. 29Eschematically depict an example of steps of a device multi-patterningmethod. In FIG. 29B, the plurality of line features 2900 is created.Then, in FIG. 29C, cuts 2920 are applied to features 2900 to yield thesegmented line features 2900 as shown in FIG. 29A.

In FIG. 29D, the plurality of line features 2910 is created, wherein theplurality of line features 2910 are created in an interleaved fashionbetween line features 2900. Then, in FIG. 29E, cuts 2930 are applied tofeatures 2910 to yield the segmented line features 2910 as shown in FIG.29A.

Thus, it may be desired to determine an overlay between the creation ofcuts 2920 and cuts 2930. Or, it may be desired to determine an overlaybetween structures 2900 and 2910. So, as will be appreciated, there canbe a variety of different overlays that could desirably be determinedand then monitored, controlled, etc.

So, the layers of interest are identified and the overlay (e.g., overlayin the X-direction, overlay in the Y direction, or both overlay in the Xand Y directions) that should be determined is identified. In thisexample, it may be desired to determine the X direction overlay betweenstructures 2900 and 2910 and determine the Y direction overlay betweenthe cuts 2920 and 2930.

So, having the one or more particular overlays of interest within thedevice, a non-product target can be designed to help determine thatoverlay. In the case of the device features of FIG. 29A, a line spacepattern of structures can be created with a comparable pitch and CD asthe layers of interest. An example of such structures of a non-producttarget design is schematically depicted in FIG. 29F. In this case, forexample, structure 2940 would be created in a same patterning process asstructure 2900 is created and structure 2950 would be created in a samepatterning process as structure 2910. As discussed above with respect toFIGS. 21-28, a physical difference can be provided between structures2940 and 2950 to enable a relative shift in the X direction whenstructures 2940 and 2950 are created to cause a break in symmetry toenable X direction overlay determination. Since structures 2940 and 2950act effectively as proxies for structures 2900 and 2910, thedetermination of the relative displacement between structures 2940 and2950 in the X direction from the radiation redirected by the non-producttarget in that condition can correspond to a X direction overlay forstructures 2900 and 2910.

Further, referring to FIG. 29G, one or more cuts are introduced to thestructures of FIG. 29F in the non-product target design to enabledetermination of Y direction overlay. To enable this, a unit cell 2960is defined. As seen the unit cell has the structures 2940 and 2950 andhas Y symmetry that is broken by the relative displacement of thestructures 2940 and 2950 in the X direction. So, to enable the Ydirection overlay determination, a feature is introduced to createasymmetry in the X direction when there is a relative displacement inthe Y direction. As noted above, it is desired to determine the overlayin the Y direction between cuts 2920 and 2930. So, comparable cuts areintroduced to structures 2940 and 2950 respectively since cuts 2920 and2930 remove portions of structures 2900 and 2910 respectively. In thisembodiment, those cuts are cuts 2970 and 2980. The cuts 2970 and 2980create a reference to determine Y direction overlay due to a relativeshift between the cuts 2970 and 2980 during their creation. Cuts 2970and 2980 act effectively as proxies for cuts 2920 and 2930, and so thedetermination of the relative displacement between cuts 2970 and 2980 inthe Y direction from the radiation redirected by the non-product targetin that condition can correspond to a Y direction overlay for cuts 2920and 2930.

In an embodiment, the cuts 2970 and 2980 are such that the unit cell issymmetric in the X direction at a nominal configuration. Further, in anembodiment, the cuts are such that they do not affect the symmetry ofthe unit cell in respect of the X overlay determination as describedabove. In an embodiment, the cuts 2970 and 2980 have comparable CD andpitch to the cuts in the device patterning process when possible.However, the size, number and location of the cuts may be adapted tomake a symmetric unit cell. In an embodiment, as shown in FIG. 29G, theunit cell is repeated as a plurality of instances to form a non-producttarget for creation on a substrate.

So, in this embodiment, at a nominal configuration, the unit cell 2960has both X and Y symmetry. Further, a relative shift in the Y directionbetween features results in a break in X symmetry in the unit cell(while Y symmetry is preserved) so that Y direction overlay can bedetermined. Also, a relative shift in the X direction between featuresresults in a break in Y symmetry in the unit cell (while X symmetry ispreserved) so that X direction overlay can be determined.

Referring now to FIG. 30, FIG. 30A schematically depicts a furtherexample of device pattern features. For example, the device patternfeatures could be for a memory device (e.g. a SRAM). As will beappreciated, a full memory device would likely have many more featuresin the area depicted. However, it may be desired to determine overlay ofa certain combination of the device pattern features depicted in FIG.30A. Such overlay can be used for patterning process control, defectprediction in the patterning process, etc. as discussed in more detailherein.

In FIG. 30A, the device pattern comprises a plurality of line features3000 extending substantially parallel to each other. Further, the devicepattern comprises a plurality of line features 3010 extendingsubstantially parallel to each other and essentially perpendicular tothe line features 3000. In an example embodiment of a multi-patterningprocess as described further hereafter, the features 3010 are createdfirst and then features 3000 are created thereafter.

Further, it is desired to have, e.g., multiple segments along a linefeature 3000. So, in a multi-patterning process, such segments can becreated by cuts as described above. So, the device pattern comprises aplurality of cut features 3020 with respect to line features 3000. Thedevice pattern features can then be created by a plurality of litho-etch(LE) processes different than, but similar to, those described inrespect of FIGS. 29B-29E.

Thus, it may be desired to determine an overlay between structures 3000and 3010. Or it may be desired to determine an overlay between thecreation of cuts 3020 and structure 3010. So, as will be appreciated,there can be a variety of different overlays that could desirably bedetermined and then monitored, controlled, etc.

So, the layers of interest are identified and the overlay (e.g., overlayin the X-direction, overlay in the Y direction, or both overlay in the Xand Y directions) that should be determined are identified. In thisexample, it may be desired to determine the Y direction overlay betweenstructure 3010 and cut 3020.

So, having the one or more particular overlays of interest within thedevice, a non-product target can be designed to help determine thatoverlay. In the case of the device features of FIG. 30A, a line spacepattern of structures can be created with a comparable pitch and CD asthe layers of interest. An example of such structures of a non-producttarget design is schematically depicted in FIG. 30C. In this case, forexample, structure 3040 would be created in a same patterning process asstructure 3010 is created and structure 3030 would be created in a samepatterning process as structure 3000. As discussed above with respect toFIG. 24, a cut can be provided to determine Y direction overlay betweena cut and an essentially perpendicular structure. That is, a cut canenable a relative shift in the Y direction between a cut and astructure, when they are created, cause a break in symmetry to enable Ydirection overlay determination.

So, referring to FIG. 30C, one or more cuts are introduced to thestructures of FIG. 30B in the non-product target design to enabledetermination of Y direction overlay. To enable this, a unit cell 3050is defined. As seen the unit cell has the structures 3030 and 3040.Further, the unit cell has a cut 3060 in structure 3030. The cut is suchthat the X symmetry is broken by the relative displacement between thecreation of the cut 3060 and the structure 3040 in the Y direction. Thecut 3060 thus enables creation of asymmetry in the X direction whenthere is a relative displacement in the Y direction between cut 3060 andthe structure 3040. The cut 3060 creates a reference to determine Ydirection overlay due to a relative shift between cut 3060 and thestructure 3040 during their creation. Since the cut 3060 and structure3040 acts a proxy for structure 3010 and cut 3020, the determination ofthe relative displacement between cut 3060 and the structure 3040 in theY direction from the radiation redirected by the non-product target inthe relative displacement condition can correspond to a Y directionoverlay between structure 3010 and cut 3020.

In an embodiment, the cut 3060 is such that the unit cell is symmetricin the X direction at a nominal configuration. Further, in anembodiment, the cut 3060 is such that it does not affect the symmetry ofthe unit cell in the Y direction. In an embodiment, the cut 3060 hascomparable CD and pitch to cut 3020 in the device patterning processwhen possible. However, the size, number and location of the cut may beadapted to make a symmetric unit cell. In an embodiment, as shown inFIG. 30C, the unit cell is repeated as a plurality of instances to forma non-product target for creation on a substrate.

So, in this embodiment, at a nominal configuration, the unit cell 3060has both X and Y symmetry. Further, a relative shift in the Y directionbetween features results in a break in X symmetry in the unit cell(while Y symmetry is preserved) so that Y direction overlay can bedetermined.

Referring to FIG. 31, an embodiment of a method to design a non-producttarget is schematically depicted. While several steps are described, notall of the steps are required. Thus, in an embodiment, a sub-combinationof the steps can be selected. Further, the order of the steps (or asub-combination of steps) could be re-arranged. Further, the designmethod is described in terms of creating a non-product target design fordetermining overlay (or any other parameter derived from the results ofsuch a target). However, the method can be extended to one or more otherparameters.

At 3100, one or more non-product targets are designed in a non-producttarget layout design process. The one or more non-product target designscan be any one or more of those described herein. In an embodiment, oneor more techniques of designing the non-product target design asdescribed herein can be used. In an embodiment, the non-product targetlayout design process primarily determines the geometry of the unit cellof the non-product target (and thus the geometry of the non-producttarget).

In an embodiment, the non-product target layout design process involvesevaluating a device pattern to identify an overlay of interest. Oftenthere are multiple combinations of features and/or layers, especiallywith LELE processing, for evaluation of overlay. So, it may be desirableto determine one or more overlay-critical combinations of featuresand/or layers.

With one or more overlays identified in terms of the features/layersbeing evaluated and the one or more directions (e.g., X, Y or X and Y),a repetitive pattern can be created (e.g., a line space pattern, anarray of closed curves such as in FIG. 28). In an embodiment, therepetitive pattern has a comparable pitch and/or CD as thefeatures/layers of interest from the device pattern.

Then, depending on the device pattern and overlay to measure, thegeometry of a unit cell of the non-product target design can be createdusing one or more of the techniques described herein. For example, wherefeatures of interest are parallel (e.g. Y direction) and overlay in theX direction is desired, then a target such as in FIG. 21 can be createdor a target can incorporate design features from FIG. 21 to enable suchoverlay to be determined. Where, for example, features of interest areparallel (e.g. Y direction) and overlay in the Y direction is desired,then a target incorporating the cut/protrusion arrangement in FIG. 22can be created or a target can incorporate design features from FIG. 22to enable such overlay to be determined. Where, for example, features ofinterest are perpendicular and overlay in the X direction is desired,then a target such as in FIG. 23 can be created or a target canincorporate design features from FIG. 23 to enable such overlay to bedetermined. Where, for example, features of interest are perpendicularand overlay in the Y direction should be measured, then a target such asin FIG. 24 can be created or a target can incorporate design featuresfrom FIG. 24 to enable such overlay to be determined.

Where appropriate and in many cases, cuts/protrusions on the lines of aline space pattern can be used as a means to break symmetry in X and/orY directions to enable respective overlays to be determined. In anembodiment, the cuts/protrusions are comparable in terms of CD and/orpitch as associated features in the device pattern. But, in anembodiment, the location of the cuts/protrusions should be such that theunit cell is symmetrical at a nominal configuration. In an embodiment,the cuts/protrusions and/or structures of the unit cell are selected tomake the unit cell as small as possible.

In an embodiment, the target need not need follow exactly all theprocess steps of the device (for example, one or more process steps ofthe device can be bypassed in forming the target if for example thosesteps are difficult to model). However, the process differences betweenthe device and the target should not impact overlay for thefeatures/layers under consideration.

When both overlay in the X direction and overlay in the Y direction aredesired from a same target, a vertical shift of the cut should notchange the symmetry with respect to the Y axis and a horizontal shift ofthe structures should not change the symmetry with respect to the Xaxis. This helps ensure that X and Y direction overlays are decoupled intheir determination from the redirected radiation from the target.

In an embodiment, if one of the layers is processed with LELE, differenttargets could be used to decouple the overlay from each of thelithography steps. If two layers are processed with LELE, then, forexample, four targets could be used.

In an embodiment, where the overlay sensitivity of the target allows it,overlay between more than two layers can be combined in the same target(e.g., a target like that in FIG. 27). This would be morespace-efficient, but there could be a loss of accuracy due to, e.g.,cross-talk or inaccuracy in the modeling due to the higher complexity ofthe target.

In an embodiment, the target should have a clearance area and apatterned area with a pattern of similar density as the device. In anembodiment, the clearance and patterned areas around the target can be,for example, at least 0.2 μm of clearance area and/or at least 2 μm ofpatterned area.

With a nominal target design, various evaluation steps can be performedto tune the nominal target design and/or determine whether the nominaltarget design will be suitable. So, for example, besides design of atarget to satisfy the overlay behavior of device features, the design ofthe target can be analyzed in view of printability (e.g., the ability ofthe target to be created as part of a patterning process), detectability(e.g., how good a signal is produced by the target), robustness (e.g.,how stable the target is to variation occurring in a patterningprocess), and/or device matching (e.g., how representative of theoverlay of the device is a determine of overlay from the target).

So, at 3110, a device matching can be performed to determine thatoverlay measured from the target is representative of the overlay of thedevice. This can be performed by using a simulator or mathematical modelto determine whether a simulated or modeled overlay of interest of thedevice matches (e.g. within a threshold) the corresponding simulated ormodeled overlay of interest of the target design. In an embodiment, thematching can be performed for a lithographic step of the patterningprocess (e.g., intrafield match). In an embodiment, the matching can beperformed for an etch step of the patterning process (e.g., interfieldmatch). If there isn't a sufficient match, the target design can be,e.g., abandoned or modified (wherein the modification can comprise achange in pitch of features of the target, a change in CD of features ofthe target, a change in material of structures of the target, etc.)

At 3120, a detectability evaluation can be performed to determine howgood a signal is produced by the target design. This can be performed byusing a simulator or mathematical model to determine to expected signalfrom the target design and whether it meets a threshold. In anembodiment, this can involve evaluation of the sensitivity of the targetto overlay, such as any of the sensitivities (e.g., a Jacobian) asdiscussed herein. In an embodiment, the evaluation can consider thepupil intensity (e.g., root mean square of pupil intensity), stacksensitivity and/or diffraction efficiency of the target design andevaluate it against a threshold. If there isn't a sufficient match, thetarget design can be, e.g., abandoned or modified (wherein themodification can comprise a change in pitch of features of the target, achange in CD of features of the target, a change in material ofstructures of the target, etc.). In an embodiment, an iteration isperformed with steps 3110 and 3120 until the respective thresholds aremet.

At 3130, a printability evaluation can be performed to determine thefeasibility of the target to be created as part of a patterning process.This can be performed by using a simulator or mathematical model todetermine whether the target design will sufficiently be produced on thesubstrate (e.g., crosses or meets a threshold). If there isn'tsufficient printability, the target design can be, e.g., abandoned ormodified (wherein the modification can comprise a change in pitch offeatures of the target, a change in CD of features of the target, achange in material of structures of the target, etc.).

At 3140, a robustness evaluation can be performed to determine howstable the target is to variation occurring in a patterning process.This can be performed by using a simulator or mathematical model todetermine whether the target design will be sensitive (e.g., crosses ormeets a threshold) to variations occurring in the patterning process andthus produce inaccurate results. For example, the evaluation candetermine the orthogonality of the target results to processperturbations by, e.g., introducing perturbations in the simulator ormodel. If there isn't sufficient robustness, the target design can be,e.g., abandoned or modified (wherein the modification can comprise achange in pitch of features of the target, a change in CD of features ofthe target, a change in material of structures of the target, etc.).

At 3150, the target can be created by a patterning process forverification of the target. A patterning process printing the target canbe set to induce various know overlay to the target and then the targetscan be measured using the techniques herein to determine overlay. Theset overlay can then be compared to the obtained overlay. If there isn'tsufficient matching (e.g., crosses or meets a threshold), the targetdesign can be, e.g., abandoned or modified (wherein the modification cancomprise a change in pitch of features of the target, a change in CD offeatures of the target, a change in material of structures of thetarget, etc.).

The determined patterning process parameter value (e.g., overlay value)and the techniques herein can be used for numerous purposes. Forexample, significant aspects to enabling a patterning process includedeveloping the process itself, setting it up for monitoring and controland then actually monitoring and controlling the process itself (e.g.,predicting a chance of a defect based on the patterning processparameter value). The patterning process parameter value and thetechniques herein can be used in any of these aspects. Further, assuminga configuration of the fundamentals of the patterning process, such asthe patterning device pattern(s), the resist type(s), post-lithographyprocess steps (such as the development, etch, etc.), it is desirable tosetup the apparatus in the patterning process for transferring thepattern onto the substrates, develop one or more metrology targets tomonitor the process, setup up a metrology process to measure themetrology targets and implement a process of monitoring and/orcontrolling the process based on measurements. The patterning processparameter value and the techniques herein can be used in any of thoseprocesses.

While discussion in this application considers an embodiment of ametrology process and metrology target designed to measure overlay of adevice being formed on a substrate, the embodiments herein are equallyapplicable to other metrology processes and targets, such as process andtargets to measure various other asymmetries in symmetrical structures,such as sidewall angle asymmetry, asymmetry in bottom floor tilt angle,asymmetries in CD, etc. Accordingly, the references herein to overlaymetrology targets, overlay data, etc. should be considered as suitablymodified to enable other kinds of metrology processes and targets.

In an embodiment, there is provided a method of determining a parameterof a patterning process, the method comprising: illuminating a substratewith a radiation beam such that a beam spot on the substrate is filledwith one or more physical instances of a unit cell, the unit cell havinggeometric symmetry at a nominal value of the parameter; detectingprimarily zeroth order radiation redirected by the one or more physicalinstances of the unit cell using a detector; and determining, by ahardware computer system, a non-nominal value of the parameter of theunit cell from values of an optical characteristic of the detectedradiation.

In an embodiment, the parameter comprises overlay. In an embodiment, themethod comprises determining an edge placement error based on theparameter. In an embodiment, optical characteristic values from pixelsof the detected radiation with greater sensitivity to a physical effectmeasured by the parameter provide a greater contribution to determiningthe non-nominal value of the parameter than optical characteristicvalues from other pixels of the detected radiation with lowersensitivity to the physical effect measured by the parameter. In anembodiment, the values of the optical characteristic form a pupilrepresentation. In an embodiment, the values of the opticalcharacteristic are processed to subtract optical characteristic valuesacross an axis of symmetry so as to reduce or eliminate the opticalcharacteristic values of a symmetric optical characteristic distributionof the detected radiation. In an embodiment, the non-nominal value ofthe parameter is determined using a summation for a plurality of pixelsof the detected radiation of an optical characteristic value for eachpixel multiplied by an associated weighting for that pixel. In anembodiment, the optical characteristic is intensity and/or phase. In anembodiment, the one or more physical instances of the unit cell is adevice structure. In an embodiment, the one or more physical instancesof the unit cell is a non-device structure within a substrate diecomprising a device structure. In an embodiment, the radiation isdetected after an etching process to produce the one or more physicalinstances of the unit cell. In an embodiment, the parameter comprisesoverlay and the method further comprises determining, from the opticalcharacteristic values, a value of a first overlay separately from asecond overlay that is also obtainable from the same opticalcharacteristic values, wherein the first overlay is in a differentdirection than the second overlay or between a different combination ofparts of the unit cell than the second overlay.

In an embodiment, there is provided a method of determining a parameterof a patterning process, the method comprising: obtaining a detectedpupil representation of radiation redirected by a structure havinggeometric symmetry at a nominal physical configuration, wherein adifferent physical configuration of the structure than the nominalphysical configuration causes an asymmetric optical characteristicdistribution in the pupil representation; processing the pupilrepresentation to subtract optical characteristic values across an axisof symmetry so as to reduce or eliminate the optical characteristicvalues of a symmetric optical characteristic distribution in the pupilrepresentation; and determining, by a hardware computer system, a valueof the patterning process parameter based on optical characteristicvalues from the processed pupil representation.

In an embodiment, the patterning process parameter is overlay and thedifferent physical configuration is a shift of at least part of thestructure relative another part of the structure. In an embodiment, thepupil representation is of primarily zeroth order radiation. In anembodiment, optical characteristic values from pixels of the processedpupil representation with greater sensitivity to the different physicalconfiguration provide a greater contribution to determining the value ofthe patterning process parameter than optical characteristic values fromother pixels of the detected radiation with lower sensitivity to thedifferent physical configuration. In an embodiment, the value of thepatterning process parameter is determined using a summation for aplurality of pixels of the pupil representation of an opticalcharacteristic value for each pixel multiplied by an associatedweighting for that pixel. In an embodiment, the optical characteristicis intensity and/or phase. In an embodiment, the structure is a devicestructure. In an embodiment, the structure is a non-device structurewithin a substrate die comprising a device structure. In an embodiment,the radiation is detected after an etching process to produce thestructure. In an embodiment, the determining comprises determining, fromthe optical characteristic values, a value of a first patterning processparameter of the structure separately from a value of the a secondpatterning process parameter, that is also obtainable from the sameoptical characteristic values, for the structure, wherein the firstpatterning process parameter is in a different direction than the secondpatterning process parameter or between a different combination of partsof the structure than the second patterning process parameter.

In an embodiment, there is provided a method of determining a parameterof a patterning process, the method comprising: obtaining a detectedrepresentation of radiation redirected by a structure having geometricsymmetry at a nominal physical configuration, wherein the detectedrepresentation of the radiation was obtained by illuminating a substratewith a radiation beam such that a beam spot on the substrate was filledwith the structure; and determining, by a hardware computer system, avalue of the patterning process parameter based on opticalcharacteristic values from an asymmetric optical characteristicdistribution portion of the detected radiation representation withhigher weight than another portion of the detected radiationrepresentation, the asymmetric optical characteristic distributionarising from a different physical configuration of the structure thanthe nominal physical configuration.

In an embodiment, the patterning process parameter is overlay and thedifferent physical configuration is a shift of at least part of thestructure relative another part of the structure. In an embodiment, thedetected radiation representation is a pupil representation. In anembodiment, the detected radiation was primarily zeroth order radiation.In an embodiment, the detected radiation representation is processed tosubtract optical characteristic values across an axis of symmetry so asto reduce or eliminate the optical characteristic values of a symmetricoptical characteristic distribution of the detected radiationrepresentation. In an embodiment, the value of the patterning processparameter is determined using a summation for a plurality of pixels ofthe detected radiation representation of an optical characteristic valuefor each pixel multiplied by an associated weighting for that pixel. Inan embodiment, the optical characteristic is intensity and/or phase. Inan embodiment, the structure is a device structure. In an embodiment,the structure is a non-device structure within a substrate diecomprising a device structure. In an embodiment, the weighting isconfigured to cause a first type of the patterning process parameter tobe determined for the different physical configuration separately from asecond type of the patterning process parameter that is also obtainablefrom the same optical characteristic values, wherein the first type ofpatterning process parameter is in a different direction than the secondtype of patterning process parameter or between a different combinationof parts of the unit cell than the second type of patterning processparameter. In an embodiment, the method further comprises a weightingconfigured to cause the second type of the patterning process parameterto be determined for the different physical configuration.

In an embodiment, there is provided a method of determining a parameterof a patterning process, the method comprising: obtaining a detectedrepresentation of radiation redirected by a structure having geometricsymmetry at a nominal value of the parameter, wherein the detectedrepresentation of the radiation was obtained by illuminating a substratewith a radiation beam such that a beam spot on the substrate was filledwith the structure and wherein, at a non-nominal value of the parameter,the physical configuration of the structure causes an asymmetric opticalcharacteristic distribution in the detected radiation representation;and determining, by a hardware computer system, a non-nominal value ofthe parameter of the structure based on a summation for a plurality ofpixels of the detected radiation representation of an opticalcharacteristic value for each pixel multiplied by an associatedweighting for that pixel, wherein the weighting for pixels in theasymmetric optical characteristic distribution are different than theweighting for pixels in a symmetric optical characteristic distributionportion of the detected radiation representation.

In an embodiment, the parameter comprises overlay. In an embodiment, thedetected radiation representation is a pupil representation. In anembodiment, the detected radiation was primarily zeroth order radiation.In an embodiment, the detected radiation representation is processed tosubtract optical characteristic values across an axis of symmetry so asto reduce or eliminate the optical characteristic values of thesymmetric optical characteristic distribution of the detected radiationrepresentation. In an embodiment, the optical characteristic isintensity and/or phase. In an embodiment, the structure is a devicestructure. In an embodiment, the structure is a non-device structurewithin a substrate die comprising a device structure. In an embodiment,the parameter comprises overlay and the weighting is configured toseparately determine a first type of overlay for the structure from asecond type of overlay for the structure, that is also obtainable fromthe same optical characteristic values. In an embodiment, the methodfurther comprises a weighting configured to separately determine, fromthe same optical characteristic values, the second type of overlay forthe structure from the first type of overlay for the structure.

In an embodiment, there is provided a method comprising: obtaining adetected representation of radiation redirected by a structure that hasgeometric symmetry at a nominal physical configuration, wherein adifferent physical configuration of the structure than the nominalphysical configuration causes an asymmetric optical characteristicdistribution in the detected representation and a patterning processparameter measures change in the physical configuration; anddetermining, by a hardware computer system, a value of the patterningprocess parameter at the different physical configuration using areconstruction process that processes optical characteristic valuesderived from the detected representation.

In an embodiment, the method further comprises processing therepresentation to subtract optical characteristic values across an axisof symmetry so as to reduce or eliminate the optical characteristicvalues of a symmetric optical characteristic distribution in therepresentation and the determining comprises determining the value ofthe patterning process parameter using a reconstruction process thatprocesses optical characteristic values derived from the processeddetected representation. In an embodiment, the reconstruction processinvolves using a mathematical model of the structure to generate asimulated representation of radiation redirected by the structure forcomparison with the optical characteristic values derived from thedetected representation. In an embodiment, the mathematical model isbased on a profile of the structure derived from measurements ofinstances of the structure. In an embodiment, the reconstruction processinvolves comparing the optical characteristic values derived from thedetected representation against a library of simulated representationsof radiation redirected by the structure.

In an embodiment, there is provided a method comprising: obtaining adetected representation of radiation redirected by a structure that hasgeometric symmetry at a nominal physical configuration, wherein adifferent physical configuration of the structure than the nominalphysical configuration causes an asymmetric optical characteristicdistribution in the detected representation and a patterning processparameter measures change in the physical configuration; anddetermining, by a hardware computer system, a value of the patterningprocess parameter at the different physical configuration using anon-linear solver that processes optical characteristic values derivedfrom the detected representation.

In an embodiment, the non-linear solver solves a function wherein theone or more variable terms thereof consist only of one or more variableterms having the patterning process parameter as the variable to an oddpower, and/or one or more variable terms having the patterning processparameter as the variable in combination with another parameter of thestructure as a variable. In an embodiment, the method further comprisesprocessing the representation to subtract optical characteristic valuesacross an axis of symmetry so as to reduce or eliminate the opticalcharacteristic values of a symmetric optical characteristic distributionin the representation and the determining the value of the patterningprocess parameter using a non-linear solver that processes opticalcharacteristic values derived from the processed detectedrepresentation.

In an embodiment, there is provided a method of configuring a parameterdetermination process, the method comprising: obtaining a mathematicalmodel of a structure, the mathematical model configured to predict anoptical response when illuminating the structure with a radiation beamand the structure having geometric symmetry at a nominal physicalconfiguration; using, by a hardware computer system, the mathematicalmodel to simulate a perturbation in the physical configuration of thestructure of a certain amount to determine a corresponding change of theoptical response in each of a plurality of pixels to obtain a pluralityof pixel sensitivities; and based on the pixel sensitivities,determining a plurality of weights for combination with measured pixeloptical characteristic values of the structure on a substrate to yield avalue of a parameter associated with change in the physicalconfiguration, each weight corresponding to a pixel.

In an embodiment, the parameter is overlay and the different physicalconfiguration is a shift of at least part of the structure relativeanother part of the structure. In an embodiment, the optical responsecomprises the optical characteristic in the form of a pupil image. In anembodiment, the optical response is of primarily zeroth order radiation.In an embodiment, the determining the weights comprises using a Jacobianmatrix. In an embodiment, the determining the weights comprises using aHessian matrix. In an embodiment, the determining the weights comprisesusing a Moore-Penrose pseudoinverse. In an embodiment, the weights areconfigured such that the value of the parameter can be determined usinga summation for a plurality of pixels of the detected radiationrepresentation of an optical characteristic value for each pixelmultiplied by the weight of the plurality of weights associated withthat pixel. In an embodiment, the optical characteristic is intensityand/or phase. In an embodiment, the structure is a device structure. Inan embodiment, the structure is a non-device structure within asubstrate die comprising a device structure. In an embodiment, themethod further comprises determining a set of measurement settings forobtaining the measured pixel optical characteristic values, the set ofmeasurement settings corresponding to the plurality of weights. In anembodiment, the set of measurement settings comprises one or moreselected from: a wavelength of a measurement beam, a polarization of themeasurement beam, a dose of the measurement beam, and/or a number ofoptical characteristic readings taken by a detector sensor of aparticular one illumination of the structure. In an embodiment, theobtaining the mathematical model comprises performing CD measurements onone or more substrates comprising the structure and calibrating themathematical model against the CD measurements to obtain a nominalprofile of the structure for perturbation of the physical configurationof the structure. In an embodiment, the method further comprisesmeasuring optical characteristic values of radiation redirected by aplurality of structures with known different physical configurations andassociated expected values of the parameter; combining the weights andthe measured optical characteristic values to determine a value of theparameter for each of the known different physical configurations; andevaluating the determined values of the parameter with the expectedvalues of the parameter; and responsive to the evaluation, adjusting aparameter of the mathematical model and/or adjusting one or more of theweights.

In an embodiment, there is provided a method comprising: using, by ahardware computer system, a mathematical model of a structure to predictan optical response when illuminating the structure with a radiationbeam, the structure having geometric symmetry at a nominal physicalconfiguration and a patterning process parameter measures change in thephysical configuration; and using, by the hardware computer system, anon-linear solver to determine, based on the optical response,coefficients of a mathematical function of the patterning processparameter as a variable thereof, the determined coefficients and thefunction for use with a measured representation of detected radiationfrom the structure, on a substrate, at a different physicalconfiguration than the nominal physical configuration which causes anasymmetric optical characteristic distribution in the detectedrepresentation, to determine a value of the patterning process parameterfor the measured structure. In an embodiment, the method comprises usingthe mathematical model to simulate a perturbation in the physicalconfiguration of the structure of a certain amount to determine acorresponding change of the optical response and wherein determining thecoefficients uses the changed optical response. In an embodiment, themethod further comprises obtaining a detected representation ofradiation redirected by the structure on the substrate having thedifferent physical configuration, and determining a value of thepatterning process parameter using a non-linear solver that processesoptical characteristic values derived from the detected representationand uses the determined coefficients. In an embodiment, the non-linearsolver solves a function wherein the one or more variable terms thereofconsist only of one or more variable terms having the patterning processparameter as the variable to an odd power, and/or one or more variableterms having the patterning process parameter as the variable incombination with another parameter of the structure as a variable. In anembodiment, the method further comprises processing the optical responseto subtract optical characteristic values across an axis of symmetry soas to reduce or eliminate the optical characteristic values of asymmetric optical characteristic distribution in the optical responseand the determining the coefficients is based on optical characteristicvalues derived from the processed optical response. In an embodiment,the mathematical model uses a nominal profile of the structure derivedfrom calibration of the mathematical model against CD measurements toobtain the nominal profile of the structure. In an embodiment, thecoefficients comprise a set of coefficients for each of a plurality ofpixels in the optical response.

In an embodiment, there is provided a method, comprising: obtainingmeasurement results for different instances of a structure generated bya patterning process, wherein measurement results are obtained at eachof a plurality of different set values of a patterning process parameterthat measures a change in the physical configuration of the structureand each different set value of the patterning process parametercorresponds to a physical configuration of the structure that causes anasymmetric optical characteristic distribution in a radiationrepresentation; and determining, by a hardware computer system, aplurality of data-driven values that correspond to weights forcombination with measured optical characteristic values of a furtherinstance of the structure to yield a value of the patterning processparameter, wherein the set values and the measurement results are usedin an objective or merit function or a machine learning algorithm, todetermine the data-driven values.

In an embodiment, the method further comprises using the determineddata-driven values to modify a mathematical model of the structure, andusing the mathematical model to derive the weights for combination withmeasured optical characteristic values of the further instance of thestructure. In an embodiment, the method further comprises using aHessian matrix of the mathematical model to update values of a nominalprofile of the structure embodied in the mathematical model. In anembodiment, the method further comprises using a Hessian matrix of themodified mathematical model to compute the weights for combination withmeasured optical characteristic values of the further instance of thestructure. In an embodiment, the measurement results are a plurality ofdetected representations of radiation redirected by the differentinstances of the structure. In an embodiment, the detectedrepresentations of the radiation were obtained by illuminating asubstrate with a radiation beam such that a beam spot on the substratewas filled with the structure. In an embodiment, the method furthercomprises generating one or more synthetic representations of radiationexpected to be redirected by an instance of the structure and expectedfor a variation in the patterning process, and wherein the determiningthe plurality of data-driven values is based on the set values, themeasurement results and the one or more synthetic representations. In anembodiment, the one or more synthetic representations of radiation aregenerated by using a Hessian matrix of the mathematical model. In anembodiment, the one or more synthetic representations of radiation aregenerated using a non-linear simulation. In an embodiment, thepatterning process parameter is overlay. In an embodiment, the methodfurther comprises determining the value of the patterning processparameter for the further instance of the structure based on theplurality of weights in combination with measured optical characteristicvalues of the further instance of the structure. In an embodiment, eachof the measured optical characteristic values corresponds to a pixel ina pupil representation and comprising determining the value of thepatterning process parameter for the further instance based on asummation for a plurality of pixels of the pupil representation of ameasured optical characteristic value for each pixel multiplied by anassociated weighting for that pixel, wherein the weighting for pixels inan asymmetric optical characteristic distribution portion of the pupilrepresentation are different than the weighting for pixels in asymmetric optical characteristic distribution portion of the pupilrepresentation.

In an embodiment, there is provided a method of determining a parameterof a patterning process, the method comprising: obtaining a detectedrepresentation of radiation redirected by one or more physical instancesof a unit cell, wherein the unit cell has geometric symmetry at anominal value of the parameter and wherein the detected representationof the radiation was obtained by illuminating a substrate with aradiation beam such that a beam spot on the substrate was filled withthe one or more physical instances of the unit cell; and determining, bya hardware computer system and from optical characteristic values fromthe detected radiation representation, a value of a first type of theparameter for the unit cell separately from a second type of theparameter for the unit cell that is also obtainable from the sameoptical characteristic values, wherein the first type of the parameteris for a different direction than the second type of the parameter orfor between a different combination of parts of the unit cell than thesecond type of the parameter.

In an embodiment, the parameter comprises overlay. In an embodiment, thefirst and second types of parameter are for different directions and fora same first and second parts of the unit cell. In an embodiment, thefirst type of parameter is for between a different combination of partsof the unit cell than the second type of parameter. In an embodiment,the method further comprises determining, from the same opticalcharacteristic values as the value of the first type of parameter isdetermined, a value of the second type of parameter. In an embodiment,the determining the value of first type of parameter uses a set ofweights for pixel optical characteristic values. In an embodiment, thevalue of the first type of parameter is determined using a summation fora plurality of pixels of the detected radiation representation of anoptical characteristic value for each pixel multiplied by an associatedweighting for that pixel. In an embodiment, optical characteristicvalues from pixels of the detected radiation representation with greatersensitivity to a physical effect measured by the parameter provide agreater contribution to determining the value of the first type ofparameter than optical characteristic values from other pixels of thedetected radiation with lower sensitivity to the physical effectmeasured by the parameter. In an embodiment, the detected radiation wasprimarily zeroth order radiation. In an embodiment, the detectedradiation representation is a pupil representation. In an embodiment,the detected radiation representation is processed to subtract opticalcharacteristic values across an axis of symmetry so as to reduce oreliminate the optical characteristic values of a symmetric opticalcharacteristic distribution of the detected radiation representation. Inan embodiment, the optical characteristic is intensity and/or phase. Inan embodiment, the structure is a device structure. In an embodiment,the structure is a non-device structure within a substrate diecomprising a device structure. In an embodiment, the detected radiationrepresentation was detected after an etching process to produce thestructure.

In an embodiment, there is provided a method of determining a parameterof a patterning process, the method comprising: obtaining a detectedrepresentation of radiation redirected by one or more physical instancesof a unit cell, wherein the unit cell has geometric symmetry at anominal value of the parameter and wherein the detected representationof the radiation was obtained by illuminating a substrate with aradiation beam such that a beam spot on the substrate was filled withthe one or more physical instances of the unit cell; and determining, bya hardware computer system and from optical characteristic values fromthe detected radiation representation, a value of the parameter forbetween a first part of the unit cell and a second part of the unit cellseparately from a value of the parameter, that is also obtainable fromthe same optical characteristic values, for between the second part ofthe unit cell and a third part of the unit cell or between the thirdpart of the unit cell and a fourth part of the unit cell.

In an embodiment, the parameter comprises overlay. In an embodiment, themethod further comprises determining, from the optical characteristicvalues, a value of the parameter for between the second and third partsof the or each unit cell or between the third and fourth parts of the oreach unit cell, separately from a value of the parameter for between thefirst and second parts of the or each unit cell. In an embodiment, thedetermining the parameter value uses a set of weights for pixel opticalcharacteristic values. In an embodiment, the parameter value isdetermined using a summation for a plurality of pixels of the detectedradiation representation of an optical characteristic value for eachpixel multiplied by an associated weighting for that pixel. In anembodiment, optical characteristic values from pixels of the detectedradiation representation with greater sensitivity to a physical effectmeasured by the parameter provide a greater contribution to determiningthe parameter value than optical characteristic values from other pixelsof the detected radiation representation with lower sensitivity to thephysical effect measured by the parameter. In an embodiment, thedetected radiation was primarily zeroth order radiation. In anembodiment, the detected radiation representation is a pupilrepresentation. In an embodiment, the detected radiation representationis processed to subtract optical characteristic values across an axis ofsymmetry so as to reduce or eliminate the optical characteristic valuesof a symmetric optical characteristic distribution of the detectedradiation representation. In an embodiment, the optical characteristicis intensity and/or phase. In an embodiment, the structure is a devicestructure. In an embodiment, the structure is a non-device structurewithin a substrate die comprising a device structure. In an embodiment,the radiation is detected after an etching process to produce thestructure.

In an embodiment, there is provided a method of configuring a parameterdetermination process, the method comprising: obtaining a mathematicalmodel of a structure on a substrate, the model configured to predict anoptical response when illuminating the structure with a radiation beamand the structure having geometric symmetry at a nominal parametervalue; using, by a hardware computer system, the model to simulate achange of a first type of the parameter of the structure to determine acorresponding first change of the optical response in each of aplurality of pixels and to a simulate a change of a second type of theparameter to determine a corresponding second change of the opticalresponse in each of the plurality of pixels, wherein the first type ofparameter is for a different direction than the second type of parameteror for between a different combination of parts of the structure thanthe second type of parameter; and based on the first and second changesin the optical response, determining a plurality of weights forcombination with measured pixel optical characteristic values to yield avalue of first type of parameter from same measured opticalcharacteristic values separately from the second type of parameter.

In an embodiment, the parameter comprises overlay. In an embodiment, theplurality of weights for the first type of parameter are determinedusing the result of a back projection of a vector corresponding to thechange in the first type of parameter in terms of the first change inoptical responses of the plurality of pixels against an orthogonal to avector corresponding to the change in the second type of parameter interms of the second change in optical responses of the plurality ofpixels. In an embodiment, the method further comprises, based on thefirst and second changes in the optical response, determining aplurality of weights for combination with measured pixel opticalcharacteristic values to yield a value of second type of parameter fromthe measured optical characteristic values separately from the firsttype of parameter. In an embodiment, the plurality of weights for thesecond type of parameter are determined using the result of a backprojection of a vector corresponding to the change in the second type ofparameter in terms of the second change in optical responses of theplurality of the pixels against an orthogonal to a vector correspondingto the change in the first type of parameter in terms of the firstchange in optical responses of the plurality of pixels. In anembodiment, the weights are configured such that the first and/or secondtypes of parameter is determined using a summation for a plurality ofpixels of the detected radiation representation of an opticalcharacteristic value for each pixel multiplied by an associated weightfor that pixel. In an embodiment, the optical response comprises theoptical characteristic in the form of a pupil image. In an embodiment,the optical response is of primarily zeroth order radiation. In anembodiment, the optical characteristic is intensity and/or phase. In anembodiment, the structure is a device structure. In an embodiment, thestructure is a non-device structure within a substrate die comprising adevice structure.

In an embodiment, there is provided a metrology target comprising: afirst structure arranged to be created by a first patterning process;and a second structure arranged to be created by a second patterningprocess, wherein the first structure and/or second structure is not usedto create a functional aspect of a device pattern, and wherein the firstand second structures together form one or more instances of a unitcell, the unit cell having geometric symmetry at a nominal physicalconfiguration and wherein the unit cell has a feature that causes, at adifferent physical configuration than the nominal physical configurationdue to a relative shift in pattern placement in the first patterningprocess, the second patterning process and/or another patterningprocess, an asymmetry in the unit cell.

In an embodiment, the first structure comprises a structure of a firstdimension and/or material and the second structure comprises a structureof a second dimension or material, wherein the feature comprises thefirst dimension and/or material being different than the seconddimension and/or material. In an embodiment, the first structurecomprises structures arranged in an array in a first direction and atleast one such structure comprises a plurality of sub-structuresseparated by voids arranged along a second direction substantiallyperpendicular to the first direction and/or the second structurecomprises structures arranged in an array in a first direction and atleast one such structure comprises a plurality of sub-structuresseparated by voids arranged along a second direction substantiallyperpendicular to the first direction, wherein the feature comprises thevoids of the first structure and/or the second structure. In anembodiment, the voids of the first structure and/or the second structureare produced using a different patterning process than the first andsecond patterning processes. In an embodiment, the first structurecomprises the voids and the second structure comprises the voids. In anembodiment, the voids of the first structure have a different pitch thanthe voids of the second structure. In an embodiment, at least one voidof the first structure lines up with at least one void of the secondstructure at the nominal physical configuration. In an embodiment, thefirst structure comprises closed curve structures and the secondstructure comprises close curve structures. In an embodiment, thestructures are arranged in the first array in a direction substantiallyperpendicular to a direction in which the structures are arranged in thesecond array or in which the structures are arranged in a third array ofstructures.

In an embodiment, there is provided a computer program productcomprising a computer non-transitory readable medium having a datastructure recorded thereon, the data structure corresponding to ametrology target as described herein. In an embodiment, there isprovided a reticle comprising a pattern corresponding to a metrologytarget as described herein.

In an embodiment, there is provided a method comprising: creating afirst structure for a metrology target, the first structure to becreated by a first patterning process that creates a correspondingdevice feature of a device; creating a second structure for themetrology target, the second structure to be created by a secondpatterning process that creates a further corresponding device featureof device, wherein the first and second structures together form one ormore instances of a unit cell, the unit cell having geometric symmetryat a nominal physical configuration; and introducing a feature in themetrology target that causes, at a different physical configuration thanthe nominal physical configuration due to a relative shift in locationof device features in the device from an expected location of the devicefeatures in the device, an asymmetry in the unit cell.

In an embodiment, a feature of the first structure has a substantiallysame dimension and/or pitch as the corresponding feature of the deviceand/or a feature of the second structure has a substantially samedimension and/or pitch as the corresponding feature of the device. In anembodiment, the feature in the metrology target causes a first type ofasymmetry in the unit cell for a relative shift in a first direction andcauses a second different type of asymmetry in the unit cell for arelative shift in a second different direction. In an embodiment, themethod further comprises evaluating one or more selected from:printability of the metrology target, detectability of the metrologytarget, robustness of the metrology target to process variations, and/ormatching of the metrology target to a device pattern. In an embodiment,the method comprises iteratively evaluating matching of the metrologytarget to a device pattern and detectability of the metrology target.

In an embodiment, there is provided a method comprising: measuringradiation redirected by a metrology as described herein transferred to asubstrate using a patterning process to determine a value of a parameterof the patterning process. In an embodiment, the parameter comprisesoverlay and/or edge placement error.

Referring to FIG. 32, a computer system 3200 is shown. The computersystem 3200 includes a bus 3202 or other communication mechanism forcommunicating information, and a processor 3204 (or multiple processors3204 and 3205) coupled with bus 3202 for processing information.Computer system 3200 also includes a main memory 3206, such as a randomaccess memory (RAM) or other dynamic storage device, coupled to bus 3202for storing information and instructions to be executed by processor3204. Main memory 3206 also may be used for storing temporary variablesor other intermediate information during execution of instructions to beexecuted by processor 3204. Computer system 3200 further includes a readonly memory (ROM) 3208 or other static storage device coupled to bus3202 for storing static information and instructions for processor 3204.A storage device 3210, such as a magnetic disk or optical disk, isprovided and coupled to bus 3202 for storing information andinstructions.

Computer system 3200 may be coupled via bus 3202 to a display 3212, suchas a cathode ray tube (CRT) or flat panel or touch panel display fordisplaying information to a computer user. An input device 3214,including alphanumeric and other keys, is coupled to bus 3202 forcommunicating information and command selections to processor 3204.Another type of user input device is cursor control 3216, such as amouse, a trackball, or cursor direction keys for communicating directioninformation and command selections to processor 3204 and for controllingcursor movement on display 3212. This input device typically has twodegrees of freedom in two axes, a first axis (e.g., x) and a second axis(e.g., y), that allows the device to specify positions in a plane. Atouch panel (screen) display may also be used as an input device.

The computer system 3200 may be suitable to function as a processingunit herein in response to processor 3204 executing one or moresequences of one or more instructions contained in main memory 3206.Such instructions may be read into main memory 3206 from anothercomputer-readable medium, such as storage device 3210. Execution of thesequences of instructions contained in main memory 3206 causes processor3204 to perform a process described herein. One or more processors in amulti-processing arrangement may also be employed to execute thesequences of instructions contained in main memory 3206. In alternativeembodiments, hard-wired circuitry may be used in place of or incombination with software instructions. Thus, embodiments are notlimited to any specific combination of hardware circuitry and software.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor 3204 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 3210. Volatile media include dynamic memory, such asmain memory 3206.

Transmission media include coaxial cables, copper wire and fiber optics,including the wires that comprise bus 3202. Transmission media can alsotake the form of acoustic or light waves, such as those generated duringradio frequency (RF) and infrared (IR) data communications. Common formsof computer-readable media include, for example, a floppy disk, aflexible disk, hard disk, magnetic tape, any other magnetic medium, aCD-ROM, DVD, any other optical medium, punch cards, paper tape, anyother physical medium with patterns of holes, a RAM, a PROM, and EPROM,a FLASH-EPROM, any other memory chip or cartridge, a carrier wave asdescribed hereinafter, or any other medium from which a computer canread.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 3204 forexecution. For example, the instructions may initially be borne on amagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem. A modem local to computer system 3200 canreceive the data on the telephone line and use an infrared transmitterto convert the data to an infrared signal. An infrared detector coupledto bus 3202 can receive the data carried in the infrared signal andplace the data on bus 3202. Bus 3202 carries the data to main memory3206, from which processor 3204 retrieves and executes the instructions.The instructions received by main memory 3206 may optionally be storedon storage device 3210 either before or after execution by processor3204.

Computer system 3200 may also include a communication interface 3218coupled to bus 3202. Communication interface 3218 provides a two-waydata communication coupling to a network link 3220 that is connected toa local network 3222. For example, communication interface 3218 may bean integrated services digital network (ISDN) card or a modem to providea data communication connection to a corresponding type of telephoneline. As another example, communication interface 3218 may be a localarea network (LAN) card to provide a data communication connection to acompatible LAN. Wireless links may also be implemented. In any suchimplementation, communication interface 3218 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link 3220 typically provides data communication through one ormore networks to other data devices. For example, network link 3220 mayprovide a connection through local network 3222 to a host computer 3224or to data equipment operated by an Internet Service Provider (ISP)3226. ISP 3226 in turn provides data communication services through theworldwide packet data communication network, now commonly referred to asthe “Internet” 3228. Local network 3222 and Internet 3228 both useelectrical, electromagnetic or optical signals that carry digital datastreams. The signals through the various networks and the signals onnetwork link 3220 and through communication interface 3218, which carrythe digital data to and from computer system 3200, are exemplary formsof carrier waves transporting the information.

Computer system 3200 can send messages and receive data, includingprogram code, through the network(s), network link 3220, andcommunication interface 3218. In the Internet example, a server 3230might transmit a requested code for an application program throughInternet 3228, ISP 3226, local network 3222 and communication interface3218. In accordance with one or more embodiments, one such downloadedapplication provides for a method as disclosed herein, for example. Thereceived code may be executed by processor 3204 as it is received,and/or stored in storage device 3210, or other non-volatile storage forlater execution. In this manner, computer system 3200 may obtainapplication code in the form of a carrier wave.

An embodiment of the disclosure may take the form of a computer programcontaining one or more sequences of machine-readable instructionsdescribing a method as disclosed herein, or a data storage medium (e.g.semiconductor memory, magnetic or optical disk) having such a computerprogram stored therein. Further, the machine readable instruction may beembodied in two or more computer programs. The two or more computerprograms may be stored on one or more different memories and/or datastorage media.

Any controllers described herein may each or in combination be operablewhen the one or more computer programs are read by one or more computerprocessors located within at least one component of the lithographicapparatus. The controllers may each or in combination have any suitableconfiguration for receiving, processing, and sending signals. One ormore processors are configured to communicate with the at least one ofthe controllers. For example, each controller may include one or moreprocessors for executing the computer programs that includemachine-readable instructions for the methods described above. Thecontrollers may include data storage medium for storing such computerprograms, and/or hardware to receive such medium. So the controller(s)may operate according the machine readable instructions of one or morecomputer programs.

Although specific reference may be made in this text to the use of ametrology apparatus in the manufacture of ICs, it should be understoodthat the metrology apparatus and processes described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or one or morevarious other tools. Where applicable, the disclosure herein may beapplied to such and other substrate processing tools. Further, thesubstrate may be processed more than once, for example in order tocreate a multi-layer IC, so that the term substrate used herein may alsorefer to a substrate that already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the disclosure in the context of optical lithography, itwill be appreciated that the disclosure may be used in otherapplications, for example nanoimprint lithography, and where the contextallows, is not limited to optical lithography. In the case ofnanoimprint lithography, the patterning device is an imprint template ormold.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g. having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

References herein to crossing or passing a threshold may includesomething having a value lower than a specific value or lower than orequal to a specific value, something having a value higher than aspecific value or higher than or equal to a specific value, somethingbeing ranked higher or lower than something else (through e.g., sorting)based on, e.g., a parameter, etc.

References herein to correcting or corrections of an error includeeliminating the error or reducing the error to within a tolerance range.

The term “optimizing” and “optimization” as used herein refers to ormeans adjusting a lithographic apparatus, a patterning process, etc.such that results and/or processes of lithography or patterningprocessing have more a desirable characteristic, such as higher accuracyof projection of a design layout on a substrate, a larger processwindow, etc. Thus, the term “optimizing” and “optimization” as usedherein refers to or means a process that identifies one or more valuesfor one or more variables that provide an improvement, e.g. a localoptimum, in at least one relevant metric, compared to an initial set ofone or more values for those one or more variables. “Optimum” and otherrelated terms should be construed accordingly. In an embodiment,optimization steps can be applied iteratively to provide furtherimprovements in one or more metrics.

In an optimization process of a system, a figure of merit of the systemor process can be represented as a cost function. The optimizationprocess boils down to a process of finding a set of parameters (designvariables) of the system or process that optimizes (e.g., minimizes ormaximizes) the cost function. The cost function can have any suitableform depending on the goal of the optimization. For example, the costfunction can be weighted root mean square (RMS) of deviations of certaincharacteristics (evaluation points) of the system or process withrespect to the intended values (e.g., ideal values) of thesecharacteristics; the cost function can also be the maximum of thesedeviations (i.e., worst deviation). The term “evaluation points” hereinshould be interpreted broadly to include any characteristics of thesystem or process. The design variables of the system can be confined tofinite ranges and/or be interdependent due to practicalities ofimplementations of the system or process. In the case of a lithographicapparatus or patterning process, the constraints are often associatedwith physical properties and characteristics of the hardware such astunable ranges, and/or patterning device manufacturability design rules,and the evaluation points can include physical points on a resist imageon a substrate, as well as non-physical characteristics such as dose andfocus.

While specific embodiments of the disclosure have been described above,it will be appreciated that the disclosure may be practiced otherwisethan as described. For example, the disclosure may take the form of acomputer program containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g. semiconductor memory, magnetic or optical disk) having sucha computer program stored therein.

In block diagrams, illustrated components are depicted as discretefunctional blocks, but embodiments are not limited to systems in whichthe functionality described herein is organized as illustrated. Thefunctionality provided by each of the components may be provided bysoftware or hardware modules that are differently organized than ispresently depicted, for example such software or hardware may beintermingled, conjoined, replicated, broken up, distributed (e.g. withina data center or geographically), or otherwise differently organized.The functionality described herein may be provided by one or moreprocessors of one or more computers executing code stored on a tangible,non-transitory, machine readable medium. In some cases, third partycontent delivery networks may host some or all of the informationconveyed over networks, in which case, to the extent information (e.g.,content) is said to be supplied or otherwise provided, the informationmay be provided by sending instructions to retrieve that informationfrom a content delivery network.

Unless specifically stated otherwise, as apparent from the discussion,it is appreciated that throughout this specification discussionsutilizing terms such as “processing,” “computing,” “calculating,”“determining” or the like refer to actions or processes of a specificapparatus, such as a special purpose computer or a similar specialpurpose electronic processing/computing device.

The reader should appreciate that the present application describesseveral inventions. Rather than separating those inventions intomultiple isolated patent applications, applicants have grouped theseinventions into a single document because their related subject matterlends itself to economies in the application process. But the distinctadvantages and aspects of such inventions should not be conflated. Insome cases, embodiments address all of the deficiencies noted herein,but it should be understood that the inventions are independentlyuseful, and some embodiments address only a subset of such problems oroffer other, unmentioned benefits that will be apparent to those ofskill in the art reviewing the present disclosure. Due to costsconstraints, some inventions disclosed herein may not be presentlyclaimed and may be claimed in later filings, such as continuationapplications or by amending the present claims. Similarly, due to spaceconstraints, neither the Abstract nor the Summary of the Inventionsections of the present document should be taken as containing acomprehensive listing of all such inventions or all aspects of suchinventions.

It should be understood that the description and the drawings are notintended to limit the invention to the particular form disclosed, but tothe contrary, the intention is to cover all modifications, equivalents,and alternatives falling within the spirit and scope of the presentinvention as defined by the appended claims.

Modifications and alternative embodiments of various aspects of theinvention will be apparent to those skilled in the art in view of thisdescription. Accordingly, this description and the drawings are to beconstrued as illustrative only and are for the purpose of teaching thoseskilled in the art the general manner of carrying out the invention. Itis to be understood that the forms of the invention shown and describedherein are to be taken as examples of embodiments. Elements andmaterials may be substituted for those illustrated and described herein,parts and processes may be reversed or omitted, certain features may beutilized independently, and embodiments or features of embodiments maybe combined, all as would be apparent to one skilled in the art afterhaving the benefit of this description of the invention.

Changes may be made in the elements described herein without departingfrom the spirit and scope of the invention as described in the followingclaims. Headings used herein are for organizational purposes only andare not meant to be used to limit the scope of the description.

As used throughout this application, the word “may” is used in apermissive sense (i.e., meaning having the potential to), rather thanthe mandatory sense (i.e., meaning must). The words “include”,“including”, and “includes” and the like mean including, but not limitedto. As used throughout this application, the singular forms “a,” “an,”and “the” include plural referents unless the content explicitlyindicates otherwise. Thus, for example, reference to “an” element or “a”element includes a combination of two or more elements, notwithstandinguse of other terms and phrases for one or more elements, such as “one ormore.” The term “or” is, unless indicated otherwise, non-exclusive,i.e., encompassing both “and” and “or.” Terms describing conditionalrelationships, e.g., “in response to X, Y,” “upon X, Y,”, “if X, Y,”“when X, Y,” and the like, encompass causal relationships in which theantecedent is a necessary causal condition, the antecedent is asufficient causal condition, or the antecedent is a contributory causalcondition of the consequent, e.g., “state X occurs upon condition Yobtaining” is generic to “X occurs solely upon Y” and “X occurs upon Yand Z.” Such conditional relationships are not limited to consequencesthat instantly follow the antecedent obtaining, as some consequences maybe delayed, and in conditional statements, antecedents are connected totheir consequents, e.g., the antecedent is relevant to the likelihood ofthe consequent occurring. Statements in which a plurality of attributesor functions are mapped to a plurality of objects (e.g., one or moreprocessors performing steps A, B, C, and D) encompasses both all suchattributes or functions being mapped to all such objects and subsets ofthe attributes or functions being mapped to subsets of the attributes orfunctions (e.g., both all processors each performing steps A-D, and acase in which processor 1 performs step A, processor 2 performs step Band part of step C, and processor 3 performs part of step C and step D),unless otherwise indicated. Further, unless otherwise indicated,statements that one value or action is “based on” another condition orvalue encompass both instances in which the condition or value is thesole factor and instances in which the condition or value is one factoramong a plurality of factors. Unless otherwise indicated, statementsthat “each” instance of some collection have some property should not beread to exclude cases where some otherwise identical or similar membersof a larger collection do not have the property, i.e., each does notnecessarily mean each and every.

To the extent certain U.S. patents, U.S. patent applications, or othermaterials (e.g., articles) have been incorporated by reference, the textof such U.S. patents, U.S. patent applications, and other materials isonly incorporated by reference to the extent that no conflict existsbetween such material and the statements and drawings set forth herein.In the event of such conflict, any such conflicting text in suchincorporated by reference U.S. patents, U.S. patent applications, andother materials is specifically not incorporated by reference herein.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the disclosure as described without departing from thescope of the claims set out below.

1.-15. (canceled)
 16. A method comprising: using, by a hardware computer system, a mathematical model of a structure to predict an optical response when illuminating the structure with a radiation beam, the structure having geometric symmetry at a nominal physical configuration and a patterning process parameter measures change in the physical configuration; and using, by the hardware computer system, a non-linear solver to determine, based on the optical response, coefficients of a mathematical function of the patterning process parameter as a variable thereof, the determined coefficients and the function for use with a measured representation of detected radiation from the structure, on a substrate, at a different physical configuration than the nominal physical configuration which causes an asymmetric optical characteristic distribution in the detected representation, to determine a value of the patterning process parameter for the measured structure.
 17. The method of claim 16, comprising using the mathematical model to simulate a perturbation in the physical configuration of the structure of a certain amount to determine a corresponding change of the optical response and wherein determining the coefficients uses the changed optical response.
 18. The method of claim 16, further comprising: obtaining a detected representation of radiation redirected by the structure on the substrate having the different physical configuration, and determining a value of the patterning process parameter using a non-linear solver that processes optical characteristic values derived from the detected representation and uses the determined coefficients.
 19. The method of claim 16, wherein the non-linear solver solves a function wherein the one or more variable terms thereof consist only of one or more variable terms having the patterning process parameter as the variable to an odd power, and/or one or more variable terms having the patterning process parameter as the variable in combination with another parameter of the structure as a variable.
 20. The method of claim 16, further comprising processing the optical response to subtract optical characteristic values across an axis of symmetry so as to reduce or eliminate the optical characteristic values of a symmetric optical characteristic distribution in the optical response and the determining the coefficients is based on optical characteristic values derived from the processed optical response.
 21. The method of claim 16, wherein the mathematical model uses a nominal profile of the structure derived from calibration of the mathematical model against CD measurements to obtain the nominal profile of the structure.
 22. The method of claim 16, wherein the coefficients comprise a set of coefficients for each of a plurality of pixels in the optical response.
 23. A method, comprising: obtaining measurement results for different instances of a structure generated by a patterning process, wherein measurement results are obtained at each of a plurality of different set values of a patterning process parameter that measures a change in the physical configuration of the structure and each different set value of the patterning process parameter corresponds to a physical configuration of the structure that causes an asymmetric optical characteristic distribution in a radiation representation; and determining, by a hardware computer system, a plurality of data-driven values that correspond to weights for combination with measured optical characteristic values of a further instance of the structure to yield a value of the patterning process parameter, wherein the set values and the measurement results are used in an objective or merit function or a machine learning algorithm, to determine the data-driven values.
 24. The method of claim 23, further comprising using the determined data-driven values to modify a mathematical model of the structure, and using the mathematical model to derive the weights for combination with measured optical characteristic values of the further instance of the structure.
 25. The method of claim 24, further comprising using a Hessian matrix of the mathematical model to update values of a nominal profile of the structure embodied in the mathematical model.
 26. The method of claim 24, further comprising using a Hessian matrix of the modified mathematical model to compute the weights for combination with measured optical characteristic values of the further instance of the structure.
 27. The method of claim 23, wherein the measurement results are a plurality of detected representations of radiation redirected by the different instances of the structure.
 28. The method of claim 27, wherein the detected representations of the radiation were obtained by illuminating a substrate with a radiation beam such that a beam spot on the substrate was filled with the structure.
 29. The method of claim 23, further comprising generating one or more synthetic representations of radiation expected to be redirected by an instance of the structure and expected for a variation in the patterning process, and wherein the determining the plurality of data-driven values is based on the set values, the measurement results and the one or more synthetic representations.
 30. The method of claim 29, wherein the one or more synthetic representations of radiation are generated by using a Hessian matrix of the mathematical model.
 31. The method of claim 29, wherein the one or more synthetic representations of radiation are generated using a non-linear simulation.
 32. The method of claim 23, wherein the patterning process parameter is overlay.
 33. The method of claim 23, further comprising determining the value of the patterning process parameter for the further instance of the structure based on the plurality of weights in combination with measured optical characteristic values of the further instance of the structure.
 34. The method of claim 33, wherein each of the measured optical characteristic values corresponds to a pixel in a pupil representation and comprising determining the value of the patterning process parameter for the further instance based on a summation for a plurality of pixels of the pupil representation of a measured optical characteristic value for each pixel multiplied by an associated weighting for that pixel, wherein the weighting for pixels in an asymmetric optical characteristic distribution portion of the pupil representation are different than the weighting for pixels in a symmetric optical characteristic distribution portion of the pupil representation.
 35. A non-transitory computer-readable medium comprising instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least perform the method of claim
 23. 36. A non-transitory computer-readable medium comprising instructions therein, the instructions, when executed by a computer system, configured to cause the computer system to at least: use a mathematical model of a structure to predict an optical response when illuminating the structure with a radiation beam, the structure having geometric symmetry at a nominal physical configuration and a patterning process parameter measures change in the physical configuration; and use a non-linear solver to determine, based on the optical response, coefficients of a mathematical function of the patterning process parameter as a variable thereof, the determined coefficients and the function for use with a measured representation of detected radiation from the structure, on a substrate, at a different physical configuration than the nominal physical configuration which causes an asymmetric optical characteristic distribution in the detected representation, to determine a value of the patterning process parameter for the measured structure. 